Ti: The state of their art



#2

Well,

I picked up (read: tried) an 89-Titanium this weekend, and must say that us hp fans have little to complain about.

My 89-Ti errata:

There is NO x^2 key (where is it? The "^" key is hardly a workaround! ALL trig functions are shifted (either left or right). That should turn away any practical engineer. The keyboard compares to the first 49g (blue). Finally, why endure all this, when it doesn't even have RPN?

I'll happily take the gold dubloon (49g+) anyday :)
EL
12345


#3

There are programs that make TIs a RPN calculator. Just google ticalc.org for RPN.

Ciao.....Mike


#4

From the documentation

"Neither Lars nor I can recommend that you use the HW2PATCH to run RPN. It is truly unfortunate
that RPN will not run on the latest TI hardware and software. Future developments may solve this
problem."

This was written in 2000! It's referring to the old TI89 - not even the new titanium edition.

It appears that the TI89 series often break things between ROM versions. Many programs rely on dirty hacks and need to be upgraded.

If you want a reliable, integrated RPN system, you still need to buy a HP. Pity about the hardware quality though.


.


#5

Yes - the TI tradition goes on with the latest Titanic ROM

HP is more reliable sans the new kb

I still take my 203MHz clocked 49g+ with 1GB SD rather that any TI.

the software simply rocks and the numerical matrix inversion is lightning fast!

(I think that even the HP-71B and the HP-28 models beat any TI)

[VPN]


#6

IMHO the discussion about using TI or HP calculators is like the talk about religion: just different ways up the mountain aiming to reach the top. Serendipitously I came across an HP-41C - otherwise I would love my old TI.

Ciao.....Mike


#7

The enduring duel goes on..

Recently, a friend commented that a classmate was almost keeping up w/ my calculations on their Ti. To which I replied, yes, with that furious parenethesis and shifting, it is obvious that they are trying to race.

RPN looks effortless, and yet is so much faster than AOS. I think artsy types would refer to that as "elegance." :)
EL


#8

Aww yes... calculator racing. In calculus and physics, classmates have just about given up trying to beat my in numeric calculations. On occasion it would be a close race when I didn't know how to directly do numberic integration without first doing an indefinite integral, but since I figured that out, its all good.

RPN really does speed things up. My friends that just use a 32sii realize that RPN is faster for arithmetic, but having never used RPN for entering equations, they have no idea half the joy.

I'm lovin' it!

-ben

#9

The calculated determinants for Hilbert matrices from order 7 through 10 as obtained with various HP and TI machines are listed below in order of increasing accuracy. All results in the table have been rounded to seven significant figures.

                           7x7              8x8              9x9             10x10            

HP-41 Math Pac 4.820822E-25 2.437673E-33 -1.605584E-42 -1.046127E-51
HP-41 Advantage 4.836648E-25 2.704536E-33 6.435130E-43 -1.747106E-52
HP-49 Nonexact 4.835583E-25 2.736296E-33 9.802414E-43 3.014075E-53
HP-28S 4.835592E-25 2.736365E-33 9.819514E-43 3.281917E-53
TI-59 ML-02 4.835807E-25 2.737082E-33 9.687516E-43 Note 4
TI-95 Math Module 4.835770E-25 2.736821E-33 9.728025E-43 2.338510E-53
CC-40/TI-74 4.835789E-25 2.736781E-33 9.689026E-43 1.898080E-53
TI-83+ 4.835795E-25 2.737004E-33 9.721266E-43 Note 5
TI-85 4.835795E-25 2.737004E-33 9.721266E-43 2.207089E-53
HP-49 Exact 4.835803E-25 2.737050E-33 9.720234E-43 2.164179E-53

Notes:

1. If you find errors in the tables let me know.

2. I do not have access to an HP-71 or a TI-89. Can someone provide those results?

3. The HP-49 Nonexact results were obtained by entering the matrix in the exact mode but pressing NUM before calculating the determinant.

4. The TI-59 ML-02 program cannot calculate the determinant of a 10x10 matrix due to memory limitations.

5. The TI-83 calculates the determinant of a 10x10 Hilbert as zero. It does not calculate the determinant of all 10x10 matrices as zero.

6. The exact determinants from the HP-49 are:

7x7:           1 / 2067909047925770649600000

8x8: 1 / 365356847125734485878112256000000

9x9: 1 / 1028781784378569697887052962909388800000000

10x10:. 1 / 46206893947914691316295628839036278726983680000000000


#10

Hi,

Just some results for an HP86B with matrix module

7x7

4.835591945E-25

8x8

2.7363743068E-33

9x9

9.82002154449E-43

10x10

3.28225800765E-53


Edited: 21 Apr 2005, 6:03 a.m.

#11

Hi, Palmer:

Palmer wrote:
" I do not have access to an HP-71 or a TI-89. Can someone provide those results?"

Download the freeware HP-71B emulator Emu71 from here at you're all set.

Best regards from V.

#12

Hi Palmer. I agree with your results for the HP 49G+ and TI-83+. By the way, thanks for the post. I learned something from it!

There may be others out there who like myself were not familiar with the Hilbert matrix. A search on google yielded the following description:

http://mathworld.wolfram.com/HilbertMatrix.html


John


#13

that despite the praise heaped upon the HP15c (and a few other HP's), in a good number of cases, the TI-59 continued to run circles around them...these matrix results being but one example.

in fact, until the exact mode on the HP49g and HP49g+, the TI-59 outperformed the HP28S and HP48 series. :-)


#14

Hi, Gene:

Gene posted:

"that despite the praise heaped upon the HP15c (and a few other HP's), in a good number of cases, the TI-59 continued to run circles around them"

You're joking, right ? Going down to the very, very, very basics, multiplication is neither commutative nor monotonic on the TI 59. Just try

               e*Pi - Pi*e    
and see what you get. Then try this same rocket-science computation in an HP-15C and marvel at the nice "0" you get. I guess it should come as a surprise to any seasoned TI user !

Now, seriously. If the TI-59 can't get its basic arithmetic right, can't you really trust all other functions that absolutely depend on it ?

And this is not a case of a contrived example, but one of an incredibly huge multitude of cases where the TI-59 basic math algorithms put themselves to shame. I challenge you to produce even one case where an HP-15C multiplication fails to be commutative (i.e. a*b # b*a) or monotonic.

Best regards from V.


#15

There are basic matrix calculations where the HP15c is several orders of magnitude LESS accurate than the built-in ML02 program in the TI-59 module.

Take a look at the Hilbert Matrix results, Valentin...the HP41 advantage module matrix code (based on the HP15C) is worse than the old TI59!

If you search through the archives, you'll find several posts by Palmer that will point out how the 15c fares poorly compared to the older TI59 ML02 program.

#16

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv014.cgi?read=59485

The HP15c's error is over 400 times larger than the TI59 in this test.

Perhaps we should say that if you can't trust the 15c beyond 5 or 6 decimal places, then perhaps it shouldn't be used? :-)


#17

Hi again, Gene:

I don't want to start a 'religious war', much less against you, but please follow the thread of your own link.

If you do, you'll see the results I gave re this case, in particular the fact that a single step of refinement (available on the HP-15C as a microcode function, for superb speed and accuracy, but nowhere to be seen in the TI-59) provided the exact result, with zero error.

You're happy with the TI-59's crappy math and the slowness of its user-code matrix programs versus the HP-15C's microcoded ones ? Good for you.

Best regards from V.


#18

Valentin, it seems you're displaying the same attitude you criticize regularly in others.

How many times here have you complained about an individual's attachment to RPN when your nice casio's produce better results?

Yet, with the Hilbert problem, it certainly appears that the TI-59 gives a better answer than the HP41 math pack, HP41 advantage pack, and the HP28S. And, since the advantage pack was based on the 15c, it seems likely that the TI59 would to beat it too.

My point is the same one you usually make but seem to have taken offense to here...

The best calculator for the solution to a problem often varies depending on the problem.

You point that out when you believe your casio's are better than an RPN machine.

But yet here... :-)


#19

Hi re-again, Gene !

Gene posted:

"Valentin, it seems you're displaying the same attitude you criticize regularly in others."

It's weekend and I'm in a playful mood, Gene ! Take no offence, man, peace !

"How many times here have you complained about an
individual's attachment to RPN when your nice casio's produce better results?"

See ? You're not paying attention ! I've never said a word about "nice casio's", I only do SHARPs (with capitals and all ...)

"My point is the same one you usually make but seem to have taken offense to here..."

Not a chance, I'm only teasing you, out of sympathy. I know you are quite sensitive in all matters TI and I just poke at you from time to time, specially when ...

"You point that out when you believe your casio's are better than an RPN machine."

... when you're not paying attention: I've got *no* casio's, I've got *SHARPs*. Repeat with me: I've got *no* casio's ... :-)

You know what ? The "problem" with you guys is that you always take me far too seriously, taking all I say at face value, so you tend to see offence, be it on your part or my part, where in fact there's none, at least as far as I'm concerned. Have a nice weekend and

Best regards from V.


#20

Yep, was in a casio mood today and that caused the disconnect. Perhaps it was because they were mentioned at the top of this thread:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv013.cgi?read=43770

which I was reading just prior to my post. Apologies in labeling you a "casio" user. BIG :-)

I do hope you saw the :-) in my post...that is my alert to you that I am certainly not mad.

It IS very interesting that in Palmer's post, the TI machines take the top spots in accuracy (other than the exact mode 49g/49g+).

Gene

#21

Howdy chaps, not that you need a hand with your math expertise and calculator prowess, but just to set the record straight, and to the extent of my necessarily limited knowledge:

The Advantage matrix functions are not based upon on those from the 15C, but rather on the CCD Module.

Maybe this is relevant to your discusion, or maybe not.

Best,
ÁM

#22

Your are, of course, correct that the TI-59 has a non commutative multiply such that e times pi is not equal to pi times e, and that HP products such as the HP-41 and HP-15 find that the products are the same. The actual results using machines in my collection are

Exact product:          8.53973 42226 73986 ...

TI-59 e x pi 8.53973 42226 73

TI-59 pi x e 8.53973 42226 45

HP-11, HP-41 8.53973 4222

I don't have an HP-15 but I will take a chance and presume that it gets the same answer as the HP-11 and HP-41. When you compare the results with the exact answer you find that error in the HP result is substantially larger than either of the TI-59 results. The values calculated for determinants of Hilbert matrices show that the TI-59 gets substantially better answers than many HP calculators which use ten or twelve digits. That's what the thirteen digits used by the TI-59 does even when using a non-commutative multiply.


#23

Let me add the results for the HP 42S and the TI-95 PROCALC:

Exact product:          8.53973 42226 73986 ...
HP 42S: 8.53973 42226 8
TI-95 PROCALC: 8.53973 42226 71

The moral: Don't count on the last digit! The relative error on both machines is directly related to the number of digits (12 versus 13).

#24

Hi, Palmer:

Palmer posted:

   "The calculated determinants for Hilbert matrices from order 7 through 10 as obtained
with various HP and TI machines are listed below in order of increasing accuracy. All
results in the table have been rounded to seven significant figures.
[...]
HP-49 Exact 4.835803E-25 2.737050E-33 9.720234E-43 2.164179E-53
[...]
2. I do not have access to an HP-71 or a TI-89. Can someone provide those results?"

Why, of course ! Here you are:

>LIST

10 ! ** Determinants for Hilbert matrices from order 7 through 10 **
20 !
30 FOR N=7 TO 10 @ P=1 @ FOR I=1 TO N-1 @ P=P*FACT(I) @ NEXT I @ Q=1
40 FOR I=N TO 2*N-1 @ Q=Q*FACT(I) @ NEXT I @ DISP N;P^3/Q @ NEXT N

>RUN

7 4.83580262391E-25
8 2.73705011379E-33
9 9.72023431183E-43
10 2.16417922642E-53

Pretty accurate, innit ? :-) Have a nice weekend !

Best regards from V.

Edited: 22 Apr 2005, 11:30 a.m.


#25

Thank you for the HP-71 results. I had tried to call up the HP-71 emulator as you suggested in an earlier transmission. I won't live long enough to figure out how to use that.


#26

I was surprised at the quality of Valentin's results since I had been told that the HP-71B used a twelve digit mantissa. When I looked at his program I concluded that it was a special purpose program which will calculate the determinant of a Hilbert matrix but has no obvious capability to calculate the determinant of a general matrix. I converted his program for use on a TI-59 and received the following results:

Order                Determinant

7 4.835802623920E-25

8 2.737050113787E-33

9 9.720234311907E-43

10 2.164179226428E-53

Pretty accurate I would say, particularly for a machine which is said to be unable to multiply properly.

Clearly, Valentin's results for the HP-71B and my results for the TI-59 using Valentin's algorithm are not "apples to apples" with the comparative results in my table. Those results were obtained with Hilbert matrices submitted to general purpose determinant solutions which are part of solutions for linear equations. So, I still need some comparative HP-71B results.


My 66 step TI-59 program is a straightforward translation of Valentin's program with a few exceptions. The Q value overflows the storage range of the data registers of the TI-59 for the tenth order Hilbert. To circumvent that problem the calculation sequence was changed as follows:

1. The P value is accumulated in a data register.

2. The cube of P is placed in the data register by recalling P and executing two PRD commands. Experienced TI-59 programmers know that this yields more accurate answers than using the y to the x function.

3. The factorials which make up the Q value are divided into the cube of the P value using the INV PRD command.

4. The answer is recalled from the data register at the end of the program.

#27

These results are for a TI Voyage 200, AMS 2.09, which should be the same as the TI-89. The Hilbert matrix entries are floating-point, and the determinant is calculated with floating-point arithmetic. Exact results for all test cases can of course be obtained with exact elements, and determinant calculation in Exact mode. The numbers in parentheses are the absolute error.

7x7: 4.8357 9853 3552 9 E-25 (4.09 E-31)

8x8: 2.7370 2158 7761 2 E-33 (2.85 E-38)

9x9: 9.7211 0716 1519 9 E-43 (8.73 E-47)

10x10: 2.1916 3783 1282 3 E-53 (2.75 E-55)

11x11: 0.0


In Exact mode the v200 can find the determinants of matrices sized up to 32x32 before 'Overflow' occurs, if you're willing to wait long enough. The determinant of that matrix is

1/342300937718736341875316480694578784160478532570744843022264
377411818016285649738348396640425838323111117643177083857527
276276421624540790363149391173439489387650276374486251367769
429081436663844014829697166121277156684389942674837249246526
267123532975018955221253356628757271358868395656787942359708
437922987111302598136409090699353808023856084601016357189208
945183452186767000583426895387929067112911767034725732791540
516268984917654473757454636544696668840459248858012619416258
814034046230919546185393229029514072344286649792394690560000
000000000000000000000000000000000000000000000000000

or about 2.92141 E-592

(12345 to delete)

#28

It seems that a somewhat subtle point in all these comparisons using Hilbert matrices is being overlooked. What I'm going to say only applies to calculators *not* in exact mode. Consider what happens when you enter the 2x2 Hilbert matrix manually. You probably enter the matrix editor on a TI or HP machine and type in 1, 1/2, 1/2, 1/3; but the calculator cannot accept exact rational numbers (fractions), so it converts these numbers to floating point numbers. The result is that you have the numbers 1, .5, .5, .33333333333333 on a TI-85 and similar recent TI machines that use 14 digits to store numbers, or you have 1, .5, .5, .333333333333 on Saturn based HP calculators.

The same thing happens for the higher order Hilbert matrices; the matrix stored in the calculator is not the exact Hilbert matrix, but an approximation to it. So when you then calculate the determinant of the approximate matrix stored in the calculator, you shouldn't expect to get the exact determinant for that particular Hilbert matrix.

What should you reasonably expect? Use a calculator that can do exact arithmetic such as the TI89 or HP49 and use these values for the Hilbert matrix (2x2 for this example):

To determine what a TI calculator which uses 14 digits to store its numbers *should* get, use
1, 1/2, 1/2, 33333333333333/100000000000000 and calculate the determinant of *this* matrix on the TI89 or HP49 (or use a PC program such as Derive, Maple, or Mathematica which can do exact rational arithmetic).

To determine what an HP Saturn based calculator *should* get, use 1, 1/2, 1/2, 333333333333/1000000000000 and calculate the determinant of *this* matrix with exact rational arithmetic.

Extend this technique for the higher order Hilbert matrices. For example, here are the last three numbers in the last row of the matrix which should be used with exact rational arithmetic to determine what a Saturn based calculator *should* get for the determinant of a 7x7 Hilbert matrix:

......909090909091/1000000000000, 833333333333/1000000000000, 769230769231/1000000000000

It isn't reasonable to expect *any* calculator which uses floating point arithmetic (and not exact rational arithmetic) to get the *exact* determinant of a Hilbert matrix because the input to the determinant calculation *isn't* the Hilbert matrix, but an approximation to it. The best it could possibly do is to get the *exact* determinant of the approximation to the Hilbert matrix which your calculator has stored. So don't compare the result a floating point calculator gets for a Hilbert determinant to the *exact* value for that particular Hilbert Matrix. You can't expect your calculator to get that result. It should in fact get the result from the procedure I described above, and you should use that result to compute the relative error for various calculator's calculated Hilbert determinants. For example, adding to Palmer's table:

                           7x7               8x8               9x9             10x10            

HP-41 Math Pac 4.820822E-25 2.437673E-33 -1.605584E-42 -1.046127E-51
HP-41 Advantage 4.836648E-25 2.704536E-33 6.435130E-43 -1.747106E-52
HP-49 Nonexact 4.835583E-25 2.736296E-33 9.802414E-43 3.014075E-53
HP-28S 4.835592E-25 2.736365E-33 9.819514E-43 3.281917E-53
TI-59 ML-02 4.835807E-25 2.737082E-33 9.687516E-43 Note 4
TI-95 Math Module 4.835770E-25 2.736821E-33 9.728025E-43 2.338510E-53
CC-40/TI-74 4.835789E-25 2.736781E-33 9.689026E-43 1.898080E-53
TI-83+ 4.835795E-25 2.737004E-33 9.721266E-43 Note 5
TI-85 4.835795E-25 2.737004E-33 9.721266E-43 2.207089E-53
HP-49 Exact 4.835803E-25 2.737050E-33 9.720234E-43 2.164179E-53
HP-41 should get 4.835822505E-25 2.709988486E-33 8.587780880E-43
HP Saturn should get 4.83558199919 2.73630981825 9.80342803933
TI-85 should get 4.8357998501314 2.7370410057623 9.7218653313429

I left out the exponents of the last two lines to save space.

HP Saturn includes the HP28, HP48S, HP48G, etc., but the HP48G and HP49 (approximate mode) will give better results than the earlier Saturn machines because the matrix arithmetic was reworked to use 15 digits for all internal matrix calculations.

According to these numbers, the relative error the TI-85 gets for the 7x7 Hilbert matrix is -1.0029e-6. The relative error for the HP-49 nonexact is 2.068E-7. This value is not quite right because Palmer reported an insufficient number of digits to accurately calculate the relative error. (There may be a similar problem with the reported results for the TI-85.) More digits would allow an improved result for relative error. The HP48G gets 4.83558259986E-25 for the determinant for a relative error of 1.24E-7 which is also what the HP49 (nonexact) gets.

Another way around the problem is to multiply a Hilbert matrix by the least common multiple (LCM) of all the denominators in the original Hilbert matrix, and find the determinant of *this* matrix. This replaces the Hilbert matrix with another which contains only integers, which can be represented *exactly* on a floating point calculator. For a Hilbert matrix of order n, divide the determinant of this "integerized" matrix by the LCM of the denominators of the original Hilbert matrix, raised to the power n, and that will be the determinant of the original Hilbert matrix. Or, just calculate the determinant of the "integerized" matrix exactly on a TI89 or HP49 (or Derive, etc.) and compare that to the result gotten from the floating point calculator.

As an example, the LCM of the denominators of the 7th order Hilbert matrix is 360360. The exact determinant of the 7x7 Hilbert matrix which has been multiplied by 360360, is 381614277072600. The HP48G gets 3.81614292044E14, for a relative error of 3.92E-8. Readers could try this on their own calculators and report the results. And beware, you can't just take the 7th order Hilbert matrix already stored in your floating point calculator and multiply it by 360360 to get the "integerized" version. In the process where you created the Hilbert matrix by inputting 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, etc., instead input 360360/1, 360360/2, 360360/3, 360360/4, 360360/5, 360360/6, 360360/7, etc. This guarantees that you get integers.


#29

My first exposure to the use of Hilbert and sub-Hilbert matrices to test the capability of matrix processing calculator mechanizations dates back to the HP vs TI competitions in the late 1970's and early 1980's as docmented in the PPC Calculator Journal and in 52 Notes (later TI PPC Notes). The idea was not that we needed the answers for the various Hilbert problems. In general, the answers were already well known. Rather, the idea was that the Hilberts provided challenging problems which could be used to assess the relative capabilities of machines and software.


#30

You say: "...the Hilberts provided challenging
problems which could be used to assess the relative capabilities of machines and software."

I'm not disputing that at all. I'm simply pointing out that when testing a calculator that doesn't do exact rational arithmetic with a Hilbert matrix, one shouldn't compare its results with the exact solution to that Hilbert matrix. The calculator couldn't get that result even if it could do *perfect* floating point arithmetic, because the matrix it's starting with *isn't* the Hilbert matrix.


#31

I am still working on your transmmission of April 24. In the process I will try to publish a table with more digits. I had done the exact work on an HP-49 loaned to me by Gene. Unfortunately I have returned it to him so I have to get the exact answers elsewhere. I may have an old multiprecision divide program which I will use if I can find it. Meanwhile I will offer comments based on my preliminary interpretation.

You seem to be saying that it doesn't make sense to compare a result from a non-exact machine with an exact result because the non-exact machine can't be expected to get the exact result. I see things another way.

I do think that comparing the result from a non-exact machine with the best results that can be expected from that machine is useful in evaluating software. I refer you to the entries in my table for the HP-41 with two different sets of matrix software; namely, the Math Pac and the Advantage packages. The entries for the 7th and 8th order determinants clearly show the superiority of the Advantage software. Other testing with Hilbert and sub-Hilbert matrices not published here shows the superiority of the Advantage software for other matrix functions as well.

But what if a potential user is deciding between machine/software combinations? Does he really much care if a machine and its software does nearly as well as it can do; that is, that the designers of the software got nearly as much out of the machine as it can deliver? I submit that he should care if the machine and its software are capable doing as much as his application requires. To make that kind of comparison the potential user needs to compare the results of the various machine/software combinations with the exact result.


#32

You said: "I do think that comparing the result from a non-exact machine with the best results that can be expected from that machine is useful in evaluating software."

I totally agree with this statement because that is exactly what I am saying. In using the Hilbert matrices to evaluate calculators, it is good to know what is the *best* a 12 digit (or 10 digit, or 14 digit) floating point machine could possibly do. What I showed in my earlier long post is just how to find the best that can be expected from an N-digit floating point calculator, keeping in mind that the best that can be done is *not* the exact result. That is an unrealistic goal for a non-exact, floating point calculator.

You said: "I refer you to the entries in my table for the HP-41 with two different sets of matrix software; namely, the Math Pac and the Advantage packages. The entries for the 7th and 8th order determinants clearly show the superiority of the Advantage software. Other testing with Hilbert and sub-Hilbert matrices not published here shows the superiority of the Advantage software for other matrix functions as well."

This is all quite true and making your comparisons with the *best* that N-digit floating point software can do rather than with the *exact* results with Hilbert matrices doesn't change any of your conclusions.

Just to give further examples, here's a table showing the relative error made by the HP48G, the HP48S and the TI-86 (which I own. It gets the same result you got for the 7x7 with the TI-83+ and TI-85). I show the relative error for the determinant of a 7x7 Hilbert matrix compared with the exact result and compared with the *best* you could expect from each of these machines. Notice that the relative error computed with the exact Hilbert determinant would indicate that the HP48G and HP48S are very similar in their results.

But the relative errors computed with the *best possible* result shows that the HP48G is substantially more accurate (that is to say, its arithmetic is better) than the HP48S for matrix determinants. In fact, the matrix arithmetic for the HP48G was reworked by Paul McClellan to use 15 digit numbers for all internal computations and is improved by more than an order of magnitude over the 48S. Even the TI is better than you would have thought by computing the relative error in comparison with the exact Hilbert determinant.

                                 HP48G        HP48S        TI-86
Rel err using exact det -4.55e-5 -4.358e-5 1.577e-6

Rel err using *best possible* 1.24e-7 2.04e-6 1.0027e-6


This table would seem to indicate that the HP48G is *better* than the TI-86. As an unqualified statement that would be false. What we *can* conclude is that the HP48G lives up to it *potential* better than the TI. In other words, the HP48G does a better job with its 12-digit arithmetic than the TI does with its 14-digit arithmetic. Neither the HP nor the TI gets what it *should* get using the arithmetic it has. I am much more familiar with the internal workings of the HP than the TI and I know that part of the reason the HP doesn't do somewhat better is that HP didn't do proper "round to even" for 15 form numbers.

All other things being equal (ceteris parabus, as the Romans would say), it is better to have more digits. The Saturn series of 12-digit calculators is *better* than the HP41's 10-digits, and the TI's 14-digit arithmetic is *better* is some ways than the HP48. It certainly returns 2 more digits for simple functions like sin, sqrt, +, -, *, /, etc. But they still don't do their basic arithmetic as well as the HP machines, and these examples of the Hilbert determinants show it, if you compare relative errors using the *best* an N-digit machine could do as your reference. So that if you work a problem that has a *lot* of number crunching, the HP48 with its 12-digit arithmetic may give a more accurate result than the TI with its 14-digit arithmetic.

In the case of the Hilbert determinant, TI has improved their arithmetic enough that the 14 digit TI-85 gets a result closer to the *exact* result than the HP48G. Since they compute the determinant with 14-digit arithmetic, we would expect that they would get a less accurate result than the HP48G which calculates the determinant with 15-digit arithmetic.

**The reason they don't is due to the fact that the 7x7 Hilbert matrix stored in the TI has 14 digits per element, so they are computing the determinant from a more accurate starting point.**

If you were to store the 7x7 Hilbert matrix in a HP48G in 15 form and then compute the determinant, you would probably get a much better result than the TI. Maybe somebody will try this.

To say that a problem is ill-conditioned is to say that it is extremely sensitive to initial conditions. That is the case with the Hilbert matrices, and that is why *starting* with more digits is more important than doing the arithmetic with one more digit.


#33

You write

"... All other things being equal (ceteris parabus, as the Romans would say), it is better to have more digits. ..."

I couldn't agree more. My first exposure to the idea came back in 1961 while working on an inertial navigation system. We observed that there was a tendency for longitude errors to go in one direction. One member of our team showed that truncation effects in our state-of-the-art 20 bit M-252 machine was the cause.

I have managed to generate the full length results (as opposed to the rounded seven digit values in my original table) for the HP-41 with the Math Pac, the HP-28, the TI-59, TI-85 and TI-95. I note that Valentin has started a new thread. I will stop entering data in this thread and move there.

#34

To the 89-Titanium's defense, it is more straightforward (though much slower) to do simple things like integrate and take a derivative or solve an equation. I rarely use mine (lent to me by the school) because it just takes so long to input equations... plus it is slow.

Of course, my 49g+ is annoying me more and more as my ON button has become unsocketed... it now moves about rather than staying put. Makes little difference, but i feel bad pressing it.

I am tempted to try and get HP to replace it, even though it is a pre-market model. Is the newer keyboard worth it, with respect to the original 49g+ keyboard?

-Ben Salinas

12345


#35

Ben,

Sorry to hear about the kbd deterioration. Here are my takes on the models I've had: The *snap* of the older ones feel better. The newer one requires less force to depress keys. The older keys are glossier, while the new keys have a rougher texture.

Are you experiencing the "other" issues, such as missed presses? I've seen much less trouble after installing the clockspeed tools (I use 124) found on hpcalc.org.

Since you've used the Ti89, how DO you square numbers in routine use? Do you have to hit the "^" key and then 2?

On the replacement issue, you could forward hp an email or call to this effect: I am grateful for the 49g+ pre-prd example. However, I have begun to experience this and that..any advice on what to do?

Best regards,
BTW, I glanced at Olin's site, sounds interesting!
Eric

12345


#36

I don't miss too many keystrokes now that I am used to using it. At first I missed a fair amount, but it is nothing a quick undo can't correct. Frankly, the 49g+ took me from hating all graphing calculators (something I mentioned just before Tony Jones, worldwide director of product development for HP, gave me the pre-release 49g+... oops), to being able to tolerate, and even enjoy using one. I definitely don't use the 49g+ to its full potential, but the features it has are wonderful (totally beat the TI-89 anyday).

When I do use the 89 (which is very seldom), I spend 3-4 times as long entering an equation because I cannot think in algebraic mode. I can't figure out, "I need to put 5 open parentheses here to make this equation work", so I always go back and put parentheses as I need them. (Plus closing parentheses is crazy). I use the ^ and 2 buttons for squaring a function.

I probably will send my 49g+ back, but probably not till after the AP exams (which start in just under 2 weeks). I will need my 49g+ for the calculus AP (no scientific calculators allowed), and for my Calc semester exam (next week). After that I won't use it again till next school year, so there will be plenty of time to mail it back.

-Ben


#37

I have also had the problem of a disconnected key on my 48gii. For me it was the 2 key that acted like a tooth about to fall out.

I could rant about the other 3 hps I have gone through in the past few months, or the one that is overdue for arrival, but suffice it to say the keyboards have not changed much since the first one (it had rom 1.22)

If you ask, you could probably get a replacement pretty quickly, by the end of this week. All except the one I am waiting for (it may not have been sent) were FedExed with a two day shipment.

-Billy


#38

Hi Billy. Have you noted the serial numbers associated with all of your 49G+'s? That information would be useful is helping to determine whether or not the keyboards are getting any better with subsequent production lots. I've got a 428... and it seems to work fine.

Regards,

John

#39

>Is the newer keyboard worth it, with respect to the original 49g+ keyboard?

Yes. The old keyboard is garbage in comparison. There are sill some missed keypressed.

.

#40

By all means ask. Hp knows about their early model problems and should do something. If it is beyond warrenty and you do not want to fight to hard, you can just pay the replair fee (you send in old calc and payment). They don't bother to repair, but replace with a new unit. Hp's repair fee is 25-50% the cost of a new calculator.

I think you should be able to get a free replacement if you whine enough, but if not, $30-60 would probably get you a new Hp49G+ which is worth it also.

#41

EL says:

"My 89-Ti errata:

There is NO x^2 key (where is it? The "^" key is hardly a workaround! ALL trig functions are shifted (either left or right). "

-----

1) What's the big deal about a x^2 key? That is a SHIFTED function on my HP-41CX, 48SX, 48G and 49G. I don't have my 49G+ or 33S handy, so I'm not sure of the situation with them.

So it takes TWO keystrokes to square a number on my HPs and it takes the SAME number of keystrokes to square a number on the TI-89/92/92+/Voyage-200. So what?

2) Granted trig functions are shifted on the TI-89. However, the big advantage of the Voyage-200 (and older 92 & 92+) over the TI-89 is UNSHIFTED trig functions.

3) My biggest objection to the TI-92/92+/Voyage-200 keyboard is that EE is a shifted function (just as it is on the lesser models of TI, such as the 83, 84, 85 & 86).

Oh well...........

--Mark


#42

I wondered about all the fuss over shifted trig functions. I looked at my TI collection and found that the great majority of TI calculators have trig functions which are not shifted. That includes the TI-30, SR-40, SR-52, SR-56, TI-68, and TI-80 through -85. The exceptions are the TI-57, TI-58, TI-59, TI-66 and TI-89. I never had noticed the difference.

I looked at my HP collection and found that the trig functions were not shifted on the HP-35, HP-45, HP-41, HP-11, etc. The trig functions are shifted on the HP-27, HP-33C, and notably the HP-67. Again, I never had noticed the difference. Does anyone really think that the shifted trig functions on the HP-67 turned practical engineers away from that device?


#43

I would guess that it depends.

If someone uses SIN or COS constantly, then it might.

But then, someone might use Y^X constantly and if it were shifted, that might make someone disappointed.

I personally think it is just one way to put an "X" against the TI89. :-)

don't get me wrong, the keyboard layout of the TI89 is not one that I particularly like, but I'm not sure shifted trig is a big problem, unless the above applies!

#44

Mark,

You stated:
So it takes TWO keystrokes to square a number on my HPs and it takes the SAME number of keystrokes to square a number on the TI-89/92/92+/Voyage-200. So what?

_______
HP's traditionally (bar the 33s) feature x^2 and x^0.5 that are assigned to the same key. Typically the square is primary and then the root is LS of the same key.

Now, you mentioned the # of keystrokes to do square a number. to square 3 on a TI requires, [3 ^ 2 ENTER], that's four strokes. Remember, you want the result, right? You must therefore count the ENTER key stroke.

On an HP, it would be [3 LS SQR], only 3 keys.

Now, if you take the root of 3 on a TI, you'd key in [3 ^ . 5 ENTER], that's five strokes versus only TWO on an HP. Plus, as the number of keystrokes increases, one is tempted to do a brain calc approx instead.

The voyager is just too large to carry around, for me. Plus I'd feel pretty childish pulling that out in an engineering class. They're (ti's) are considered high school gaming machines around my circles. But, enjoy the calc you like.


That's two cents I can afford to lose :)
EL


#45

I was at WAL-MART today and saw an HP-33S in their calculator display. The first thing that I noted was that the keyboard in not laid out in a rectangular grid but the old horizontal rows have been changed into arcs. Then I noticed that the TI-84 Plus also has the old horizontal rows changed into arcs. What is that all about? My best guess is that it has something to do with the younger calculator users. I have heard that they no longer hold their calculators in the palm of one hand and press the keys with the index finger of the other hand, but rather hold the calculator between their hands and press the keys with their thumbs as they learned to do when playing games. Is that really what they do? Is the keyboard layout of the HP-33S and TI-84 Plus the wave of the future?


#46

"... Is the keyboard layout of the HP-33S and TI-84 Plus the wave of the future?

Oh, boy! I hope not. I got used to the 33S, but hope later models will reincorporate the more traditional layouts.

#47

I think the typical calculator usage scenario for the younger users (= high school students) has the calculator lying on a table, surrounded by other clutter like paper and pens etc., and being used without being held in the hand.

Speaking personally, when I use a calculator while holding it in my hand, I usually hold it in my right hand and press the keys with my right thumb. On the Woodstocks and 41 that works fine; for the Voyagers and 42S, I do what you described: I hold the calc with both hands and use both thumbs (unless I'm just doing basic arithmetic: then all the keys I need are within reach of my right thumb).

This has nothing to do with playing games -- I do own a Game Boy, but I was using calculators long before that (I'm 40). I think the "chevron" key layout is just a gimmick to make the 33S look "cool". I'm sure it's successful -- this is what you do when targeting a demographic that buys colored face plates for their cell phones!

- Thomas


Possibly Related Threads...
Thread Author Replies Views Last Post
  HP Prime reset to factory state? BruceH 3 1,110 11-26-2013, 07:27 PM
Last Post: BruceH
  TI Selling new TI NSpire Touchpad Namir 9 861 04-20-2010, 06:20 PM
Last Post: Bart (UK)
  State of the art Walter B 12 921 03-20-2008, 01:12 PM
Last Post: designnut
  Comparing Ti 89 Titanium vs. Ti 84+ SE vs. Hp 50g PhysicsNerd 16 1,147 01-05-2008, 10:37 AM
Last Post: EL
  Communicating stack state transitions, a notation. Arne Halvorsen (Norway) 7 742 10-10-2007, 01:43 PM
Last Post: Arne Halvorsen (Norway)
  difference between TI-Nspire and TI-Nspire CAS Don Shepherd 7 676 08-05-2007, 07:41 AM
Last Post: Don Shepherd
  TI-Nspire, TI-Nspire CAS, early Prototype Joerg Woerner 3 423 07-25-2007, 02:03 PM
Last Post: Joerg Woerner
  HP49+ - Backing Up Calculator State Les Wright 9 739 04-27-2007, 04:18 AM
Last Post: Les Wright
  TI USA Warming up for new TI NSpire Calculator Namir 4 503 09-12-2006, 11:45 AM
Last Post: Jeff Wolfe
  (OT) HP Owner's Handbook Cover Art Trent Moseley 1 283 08-25-2006, 02:19 PM
Last Post: Raymond Del Tondo

Forum Jump: