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A colleague has emailed me a link to this talkback post, which I'm relaying here:

http://www.zdnet.com/5208-10533-0.html?forumID=1&threadID=7786&messageID=156250&start=-43

It's pretty clear, and provides some interesting insight. There are links to the original blog post and other talkbacks at the bottom.

Best,
--- Les

[http://www.lesbell.com.au]

Les --

Pretty good and insightful "blog commentary". His central point reminds me of a more fundamental one.

Why is it that many people praise CEO's who run their vast enterprises as though they were merely a set of independent companies? This philosophy, associated with Jack Welch (formerly CEO of General Electric) asserts that each division chief is responsible for the profitability of his unit. Unprofitable divisions can then be sold, or at least placed under the stewardship of CEO's with an eye on the bottom line.

This approach ostensibly promotes accountability and delegation of authority. Maybe so, but it also fails to recognize that certain endeavors usually need to be nurtured or revitalized through investment before profitability is even possible. If every division must make money now, where do tomorrow's money-makers come from? A corporation can't expect to simply acquire every productive asset, any more than a pro sports team can expect to build a perennial contender through free agency.

GE has certainly been profitable, but what mainstream mass-market products are they known for today? Not TV's and other consumer appliances anymore -- those markets were ceded long ago. They are still big in the electric-power industry, making turbine-generators, transformers, and other high-voltage equipment. Jet aircraft engines are also a major business, and GE also provides consulting services. The other primary GE businesses that occur to me, however, is GE Capital.

Not everyone is enamored with the Welch approach. Several years ago, a rather uncomplimentary book was written about his tenure at GE.

-- KS

Hi Les Bell, all;

I don't remember reading about so many good points related to the main title theme in one single text. I'm not in condition to critize, support or be against because I have no additional information, but the text is so well constructed and so easy to read that I searched for more of it after reading it all; in fact, I read it more than twice (it's worth).

The text ends with a supperb:

Quote:
HP is now a Digital Entertainment company … give me a break.

It's worth reading. Now I'm gonna read the contents of the additional links. Thanks, Les Bell!

Cheers.

Luiz (Brazil)

Hi, Karl;

Quote:
If every division must make money now, where do tomorrow's money-makers come from? A corporation can't expect to simply acquire every productive asset, any more than a pro sports team can expect to build a perennial contender through free agency.

Please, this is exactly what I think, no pun intended at all: why do people with the kind of thought you expressed here are not actually running enterprises as CEO's? It's so "crystal clear", and it seems some CEO's don't (want to?) see.

I see that many of my students are already finding a way to promote sales while they are studenst. O.K., no problem with the choice, but they are supposed to be graduating as technicians, not salespersons. Please, no priviledge or misregarding, just a matter of choice. The R&D staff must be aware of the fact that whatever they are developping must be taken as part of a final product, either as a component or as an enhancement. But they should not be spending time with computing the profits related to their effort on doing that because they'd be comsumming time on doing something they are not actually supposed to be doing. The same would happen if profits are running low and administrative staff decides to invade R&D labs in search for new discoveries that can be sold, somehow...

I sometimes tell my students that as soon as someone builds something, commerce goes ahead. If everyone decides to run 'profitable businnes' based solely on buying and selling, soon there will be no goods to be sold or bought because there is no one taking care of their production. And if there is a production line and no enhancement, improvement or some brand new "gadget" to be added, we'll be buying and selling the same stuff till mankind exists.

Oops! I think that as an Elect. Engineer I have gonne a bit far.

Blames? Flames? Comments?

Luiz (Brazil)

there's quite a depth carley hp feature in fortune this week.
www.fortune.com

...as you be judged first!

I was wondering: is there anybody else beyond the members of this forum who is concerned about quality yet?

As I can see: everything is "Made in China". The prices are very low and the quality, usually, is too.

When you go to a store buy a new gadget, there is always a "this does the same thing (similar)" chinese close by it with a 25% cut off.

I assume that I'm always tempted to buy the chinese one. After all, if it break, I can buy a new, and other, other, other ...

It may be this the thoughts in the CEO's heads. Do not produce nothing (as it is produced in China), sell as many as they can, have high profits, but no care with the employments in their own country.

I know my thoughts are very simple in this confuse world.
Artur

Buying cheap, breakable junk is a losing economic model. Good examples:

Hi quality lamp, metal parts, $50 in 1980, still works, will always work.

-vs-

Cheap lamp, plastic parts, $10 2000, broken in 1 month, so 12 of them a year.
Which makes better economic sense?

Or,

11c, $120, 1983, lasted until lost in 1995.
30s, closeout, Staples, $4.50, ususally $15, 2004, quit working properly in two months (loses memory if you allow the case to be flexed at all). Same for replacement. So, 12 * $15 for every year.

Tubular bicycle tire, (Tufo) made in Czech republic, $40 current dollars, lasts 1800 miles average, after using 10 of them, no premature blowouts, but one sidewall cut blowout; all others survive until the threads are showing.

Tubular tire, (Vittoria) made in Indonesia, $12, average lifespan, 250 miles, about 1 in 8 blow out the first day.

Hi quality colander, copper plated steel, $50 if would replace in 2004 dollars, lasted 25 years, still going strong, vs

Aluminum colander, $4.99, made cheap, lasts 1 year before feet & handles break off.

And I am sure I can come up with dozens more.

Which ones make better economic sense?

Regards,

Bill

Edited: 2 Feb 2005, 10:40 a.m.

When we started to import stuff from China in the late 80's and early 90's, the quality of these products were very bad and their prices were very low. Today the quality isn't all that bad and the price is up about what it used to cost for the US made stuff. In the future, I believe the quality of these Chinese products will be high and their prices will be extra-ordinary high. In the end all we did was to give away to the Chinese our industries.
As the footnote, NO I never felt tempted to buy Chinese made stuff even though they were cheap. Today, I don't want to buy them either even though at least on a number of products their quality while not high is OK. No, I don't want to buy them in any cases but many times that is the only choice.

Hi, Bill:

Bill posted: "Which ones make better economic sense?
"

It depends to whom you're asking the question or where you ask the question.

Most people will do whatever it takes to save a cent, even if it means a lower quality product and they know it. Very few people bother to do the math you mention to realize that a seemingly present gain is actually a loss in the long run. So, garbage products (such as KinHPo calculators) are the order of the day.

As for further examples, here's one of my own:

A SONY discman player (can't remember the model, probably
a D-5) I bought in the early 80's, square, all-metallic, rock-solid feeling. It's been playing at least 1 hour a day since then (many times 4 hours or more, I sleep very little), yet still works, looks and sounds absolutely perfectly (after some 10,000+ hours playing !!); cosmetically it would easily pass for new, and
can drive enourmous headphones at incredible volumes with top-quality sound.

Compare that to the latest, "made in China" models, all-plastic, feeble things, made with the cheapest components the manufacturer's money can buy, much noisier in operation, worse sound, will distort if used with said headphones, will typically last a year or two before something breaks or wears.

In short: Quality comes at a premium, but most people would rather buy cheap than wise. There's quite an appropriate Spanish proverb for this kind of folly, which reads like this:

     "No está hecha la miel para la boca del asno"
which literally translates as
     "Honey wasn't meant for donkeys"

and is essentially the same as the English proverb:

      "You're casting pearls before swine"

Best regards from V.

I must agree with all of you.
I'm not one that buy things only for their value, but usually I look for some quality in them. So, I'm still an 11C, 15C, 41C lover.
About chinese things, I must apologize. After all, many things made there are very cool, as many made here in Brazil. Actually, I have very fine electronic equipment from China and they are perfectly. The point of view is actually the low quality project on new HP calculators. If they take care a bit more on details, such keyboard, painted labels and other small things, certainly the chinese industry could make them as planed.
Other point is about work places. I may be wrong, but, making things outside your country doesn't contribute for less employment?
Just small feelings...no offense at all, ok?
Artur

I like that Spanish proverb and will remember it well.

While most of us here appreciate a quality calculator, the world in general does not consider a calculator a tool for their profession. It is something to be used on occasion to check their bookwork and any $3-5 calculator will work. They put such low value on these that they are considered disposable. Math is a chore that has to be endured once a month (as if we consider this MATH?) when paying bills.

Therefore, we endure the blank stares of unbelief if we admit our calculator affection or try to justify the purchase of a $50+ or greater purchase for a calculator to people who KNOW you can buy a great little scientific for $10-20.

And a question for anyone with a Casio fx115MS. I am using this as my backup to an Hp33s for the upcoming PE exam. I was checking out its numerical integration and I am probably entering something wrong as it is failing miserably in a simple integral.

integrate SQR(4-x^2) from 0 to 2.

Perhaps I am not inputing the variable or the lower, upper limits in the correct sequence. I have tried in various modes ie Radians vs Degrees etc. Any hints or info. I do not even get consistantly WRONG answers. I have used this before on other integrals and did fine in the past (also simple integrals and quite a bit further back in my memory and time).

"And a question for anyone with a Casio fx115MS. I am using this as my backup to an Hp33s for the upcoming PE exam. I was checking out its numerical integration and I am probably entering something wrong as it is failing miserably in a simple integral."

I advise you to purchase a second HP-33S as your back-up. I bought two of them for that purpose (I took the exam just last October); here's how I worked it (I passed my PE, btw! Yay for me!):

1. I kept one HP-33S at work and used it every chance I had (i.e., all the time).

2. I kept the other at home for studying. I marked each calculator with a Sharpie marker, indicating which was the home one, which was the work one. I memorized which programs I had on which (essentially, both had interpolation programs). I didn't bother putting the same programs on each calculator because most, if not all, of the problems I'd encounted while studying (and on the test!) did not really require "programs" - except maybe for surveying problems (I took the Civil P.E.).

3. I brought, naturally, both with me to the exam - with, naturally, extra batteries. I had both calculators on my table and realized an hour into the exam that I was using them interchangably. I also felt super confident that if one failed I'd have no problem picking up the other and just continuing if nothing happened.

While I may consider that option, I really don't need an extra Hp33s (it actually irritates me to use it as I would rather take an Hp42s, but since that calculator was specifically banned and I do prefer RPN, I will take at least an Hp33s). But I am also a stubborn mule who is just as apt to take a slide rule, since the NCEES has now made a list of about six calculators that are ONLY allowed. I had planned to just take an older Hp32s and an Hp15c (or maybe a Ti66). IF it weren't such an important TIMED exam, I would take in a four function calculator (which isn't on their list either) and a trig and log table, but the person who would suffer from such arrogance would be ME!

I have NEVER seen anything from Red China that has equal quality to equiv. non-Chinese product. Biz model is low quality + thin profits X mass sales. Clearly not 'built to last'; everything seems disposable.

This applies to electronics, clothing, kitchenware, etc.

Electronics made in China isn't as good as that from Taiwan, Indonesia, etc. Board quality, connector quality, power supply quality are often substandard. Shirts from China seem to not last too many wash cycles compared to those from India etc. Plus China has NO idea about clothing in XL or XXL sizes, nor do they take the effort to find out! Cups and saucers break easily, etc. etc.

Totally aside from quality issues, I generally avoid buying any Red Chinese products as many of us in the USA perceive China as an enemy country we just happen, unfortunately, to do business with -- WalMart being the funding agency for Red China's military modernization.

I do carefully look at country of origin of what I buy. I myself try to buy American or European products or real quality made-in-Japan products. Or from neigboring Mexico/Latin America - maybe sending some biz there might help some of our illegal immigration issues, dunno... My goal is to generally purchase from somewhat reputable companies civilized societies, not bottom feeders from countries where starving people and dirty civilian water supply is regarded as 'competetive advantage'.

Sometimes it is hard but you can do it. I, for example, will not buy anymore Durango cowboy boots - all Chinese made now. Same with Levi's jeans - I buy Lee or Wrangler pants marked Made in USA (not all variants are). Quite a few of my dressier pants I buy are made in Indonesia or Bangladesh but at least not Red China. My Philips projection TV set has European and Taiwanese chips but is assembled in USA. My Sony home theatre system is actually made in Japan, not China. Most of my guns are made by Smith&Wesson, Colt or Ruger. Ford makes my truck and has a high Western (USA+Canada+ Mexico) parts content. I buy quality US- or European-made dress shoes and keep care of them+repair them, instead of wearing throwaway Chinese cheapies. Keeps the shoe man in business too (finding a good one skilled in leather work is hard these days!!)

Oh - my underwear and socks are US made too. My PC motherboard is made in Taiwan, with hard disk assembled in Mexico.

Sorry to bore you all with this litany but it is possible to do as little biz with Red China as possible at least on a personal scale. It can vary, and sometimes there's no option. (I couldn't find a US-made Thermos-style vacuum bottle for my coffee.) But I generally think you'll be happier with quality by "going elsewhere". It takes just a bit of effort.


Bill Wiese

San Jose CA USA

I'd rather pay a higher $$ amount for something that will last a longer than pay cheap only to have to replace it the next day. I also find that I stick with the higher quality products. Case in point: I had to go through two (!) HP49G+s before I found a decent keyboard.

The challenge is that 90% of everything sold in the U.S. is made in China.

Quote:
Why is it that many people praise CEO's who run their vast enterprises as though they were merely a set of independent companies? This philosophy, associated with Jack Welch (formerly CEO of General Electric) asserts that each division chief is responsible for the profitability of his unit. Unprofitable divisions can then be sold, or at least placed under the stewardship of CEO's with an eye on the bottom line.

Exactly. And what is even worse, is that in such a structure, the purpose of the CEO is to act as a figurehead - someone who is able to see deeper than the usual bean-counting MBA approach to management. We expect a CEO (or Chairman of the Board) to be *the* person who can say "No - this area is going to be significant, so let's keep investing in it because we *will* see a return in time", or "Our customers expect high quality products, and shifting production to an outsourced factory in S.E. Asia is going to damage our reputation and subsequently our bottom line".

But in many cases, as you observe, CEO's are not providing that kind of leadership at all. And specifically at HP, I suspect the corporate culture has been replaced by a collection of consolidated spreadsheets.

Best,

--- Les

[http://www.lesbell.com.au]

Absolutely agreed.

I remember that, back in early 1976, when I bought my HP-65, I was reading "Zen and the Art of Motorcycle Maintenance", which is entirely about the definition of quality. I even remember reading it on the train while heading out to HP's Canadian office which (IIRC) was out in Mississauga, west of Toronto.

As I debated Pirig's assertion that quality is undefinable, the object that, to me, represented Quality was my HP-45 (and the 65 I would shortly buy). To me, the mechanical construction, the logical design, and the accompanying documentation all represented something that was well above some kind of "minimal scientific calculator".

For a while, I thought quality might be defined as work over and above that required to construct the minimal product, but the problem is that some designers can work hard to reduce the quality of the product by making it too complex or otherwise ill-fitted to the task. In the end I pretty much agreed with Pirsig - I can't define quelity, but I know it when I see it.

And I'm not seeing it in HP's products these days.

Best,

--- Les

[http://www.lesbell.com.au]

Quote:
Which ones make better economic sense?

Ummm . . for the company that hopes to get an ongoing revenue stream without having to invest significantly in produce design and manufacturing plant, the cheap rubbish is the obvious way to go. Otherwise, there wouldn't be so many of them doing it.

Of course, for the rational consumer, quality is the way to go. Unfortunately, there's a shortage of rational consumers, and increasingly a shortage of quality products.

Best,

--- Les

[http://www.lesbell.com.au]

I too avoid buying from Red China, and find it
increasingly difficult.

But I'm also a guilty one.
Back in the '80's and early '90's, I enjoyed buying
Cheap Chinese Crap. I was young with a small income,
and my money seemed to go farther with CCC.
I had a double agenda, I believed that buying from
China would encourage them to become more capitalistic,
less communistic and improve human rights in China.
The other side of this agenda, I wanted
the overpaid Union workers in the US who made crappy
Fords and Dodges and stereos and et cetera to shape up.

But China hasn't changed its human rights record for the
better one iota. Now they are building the crappy stuff,
and Union workers are out of a job.
So now it is harder to find work in
my chosen profession because their is so little electronics
manufacturing (or repair) in the US.

Yes, the Unions did get a message, too little too late.
And now I'm simmering in the pot of stew I helped make.

But I'll buy Sears Craftsman Lifetime Warranteed tools,
and often leave the CCC on the shelf.

Molecular scale transistor??

http://www.nytimes.com/2005/02/01/technology/01nano.html?oref=login

Pio

Ahh, you mean this?

That's interesting, but it remains to be seen whether they can incorporate it into a product with a reasonable level of quality. That's a development problem, not a research one.

Best,

--- Les

[http://www.lesbell.com.au]

Ron --

I agree with your thoughts about quality.

Now, about the integration problem you specified:

INTEG (sqrt(4-x2) dx between 0 and 2

On the Casio fx-115MS, the user enters the expression to be integrated after the integral sign, followed by (and separated by commas) the lower limit, upper limit, and # of partitions as an integer power of 2. "=" gives the answer.

Some things to remember:

  • The variable of integration must be X. All other variables will simply be employed using their current values, which might cause a "Math Error".
  • If the integrand is undefined at a limit or interior value, "Math Error" will result, and the user must start over.
  • The fs-115MS uses Simpson's Rule (as have all inexpensive Casios over the years). The calc will return only the number of significant digits it deems justifiable, then fills out the selected display precision with zeroes.

So:

[Sdx]
[sqrt]
(
4
-
[ALPHA]X
[x2]
)
,
0
,
2
,
9
)
=

will give the best answer it can, with 513 function evaluations under Simpson's Rule (29 +1 ) : 3.1416

By contrast, the HP's Romberg method used by the 15C, 33S, and other models gives answers much closer to the exact answer of pi, in much less time. Romberg is much better than Simpson for this problem.

-- KS

Edited: 3 Feb 2005, 4:17 a.m.

Les,

IMHO the best definition is: "Quality is meeting (and possibly exceeding) your customer's expectations." It includes the ambigity you mentioned.

Since nowadays 99.x% of perspective calculator users did never have a chance to experience a rock solid scientific calc anymore (which many in this forum remember very well, or even possess), they simply cannot have an idea of such a device. So they will not expect something like this. This runs in parallel with the low prices mentioned in this thread several times. You can't expect too much quality for this.

The times many of you remember, good calculators used to cost more than some 100 $ or equivalent in other currencies (yeah, they still exist!). I remember to have paid more than 600 DM in 1974 or 75 for my first calc (a TI SR 50, since HP was far out of my budget). Being a university student, this was a fortune at that time! But the calc was faster than a slide rule combined with math tables and eased my studies quite a bit. So guess what I would have done if my precious would have failed after a year or so?! I would have had to save money for quite some time until I could afford a new calc. It took me 3 years and some work as teaching assistant to buy a repaired HP25C. Therefore, those calcs simply had to be rock solid to give you a return on your investment. Nowadays, they are no investment anymore. Such, this closes the cycle ...

Just my 0.01 € (Euro)

Hi, Karl:

Karl posted:

"[...] will give the best answer it can, with 513 function evaluations under Simpson's Rule (29 +1 ) : 3.1416. By contrast, the HP's Romberg method used by the 15C, 33S, and other models gives answers much closer to
the exact answer of pi, in much less time. Romberg is much better than Simpson for this problem.

The HP-71B Math ROM's keyword INTEGRAL uses essentially the same Romberg-based algorithm as the HP-15C, and, right from the keyboard (no program) very quickly produces this:

>INTEGRAL(0,2,1E-7,SQR(4-IVAR*IVAR)) , PI

3.14159265359 3.14159265359

accurate to 12 places, using just 63 function evaluations, i.e., it produces nearly 3 times as many decimal digits with 8.14 times less evaluations than the much inferior algorithm used in the Casio.

Of course, comparing the ultra high-quality, state-of-the-art math algorithms designed for and implemented in the HP-71B Math ROM versus the ones in any Casio machine is pretty preposterous to begin with, just have a look at my article "Baker's Dozen" in the very next Jan-Feb 2005 issue of Datafile, which discusses a number of interesting topics, quirks, and powerful uses of the Math ROM.

P.S.: As for integration methods, I'll take Gaussian adaptive methods over Romberg any day. One of
the main reasons it isn't used by HP in their calculators is simply because it requires a *large* number of full-precision constants, which is expensive in terms of ROM space. That's why they selected some Romberg's variation though fully aware that Gaussian methods were best (i.e., much less evaluations for any specified accuracy).

Actually, even Gaussian quadrature is becoming obsolete. Cutting-edge numerical math researchers now favor the relatively new Error Function quadrature and Tanh-Sinh quadrature schemes, which are even faster and more robust than Gaussian quadrature while remaining reasonably easy to implement.

Best regards from V.

Edited: 3 Feb 2005, 7:31 a.m.

.

Thanks for all that interesting extra information.

Above, I did not know that you should only integrate with X on the Casio. My own problem was that I place X in the spot where you place the interation number. And the Casio is sloooow. But it will work as a back up in case the new fangled Hp33s happens to fail. And while I could just buy another Hp33s, I feel confident enough with the Casio as a back up (passing or failing won't (and shouldn't) depend so much on the calculator, but on myself, BUUUT I will blame that POS anyway, should I fail!!!)

]Bop

Hi, Valentin --

Thank you for the informative follow-up to my post. I have to admit that I still haven't gotten a Math ROM for the HP-71B I bought on eBay more than a year ago. The ROM itself seems pretty hard to get -- I've never seen it appear on eBay or the MoHPC Classifieds as an individual item.

Not having yet posted a "WTB" ad, though, I can't really complain. I'm not even sure what a fair price is, but the amount that might be asked would probably be sobering.

As for Casio's methods, I'm only speculating. My fx-3600P from 1981 uses Simpson's, as does the 2004 fx-115MS, so I assume that all their low-end models did.

Hi, Karl:

Karl posted:

"Thank you for the informative follow-up to my post."

You're welcome. If you want to know more, have a look at this very interesting PDF document discussing all three methods, with pretty challenging examples:

A Comparison of three high-precision quadrature schemes

"I have to admit that I still haven't gotten a Math ROM for the HP-71B I bought
on eBay more than a year ago. The ROM itself seems pretty hard to get -- I've never seen it appear on eBay or the MoHPC Classifieds as an individual item."

Yes, it's a real gem, a much valued and sought-after add-on among knowledgeable HP-71B fans. However, it actually isn't that rare, there are tens of thousands of them still in existence, because it was bundled with a very large order of HP-71Bs by a British (IIRC) health care organization, and when the machines were replaced, their Math ROMs went with them.
Myself, I have three HP-71B and each one of them came with their own Math ROM included.

Anyway, if you're eager to try it, or the examples I post or some of my articles about it (i.e.: "Baker's Dozen" in the next Datafile issue), just get Emu71 from Jean-François Garnier, it comes complete with the Math ROM image and all, and it's absolutely free, very convenient to use, and runs at awesome speeds (25-30x times the speed of a physical HP-71B), which makes the Math ROM functions all that more powerful.

Or, if you have a 48/49 model, you can get HP-71X from Hrastprogrammer, which will give you full 71B compatibility with the added bonus of portability, at 2x-3x the speed of a physical 71B.


"Not having yet posted a "WTB" ad, though, I can't really complain. I'm not even sure what a fair price is, but the amount that might be asked would probably be sobering."

Can't say. As stated, I just bought the 71B's and the Math ROM was included as well (together with the HP-IL ROM; it was bundled with them, too). I got the machines for prices around $100 (i.e., HP-71B + HP-IL ROM + Math ROM), virtually mint.

"As for Casio's methods, I'm only speculating. My fx-3600P from 1981 uses Simpson's, as does the 2004 fx-115MS, so I assume that all their low-end models did."

I'm convinced that only HP engineers of the golden age actually cared about the quality of their algorithms. I know for sure that both the HP-15C and the HP-71B Math ROM were incredible tours de force with engineers, programmers and numerical-algorithms experts racking their brains to the most to achieve the maximum speed, accuracy, range and, of course, functionality in the allotted ROM space. As such, the HP-71B Math ROM is the most optimized, higher quality 32K of Saturn assembler programming ever written, bar none. Everyone of the many incredibly gifted people involved in its creation loved what they they were doing, and it shows.

Best regards from V.

Hi Valentin, folks;

I cannot help quoting this:

Quote:
I'm convinced that only HP engineers of the golden age actually cared about the quality of their algorithms. I know for sure that both the HP-15C and the HP-71B Math ROM were incredible tours de force with engineers, programmers and numerical-algorithms experts racking their brains to the most to achieve the maximum speed, accuracy, range and, of course, functionality in the allotted ROM space. As such, the HP-71B Math ROM is the most optimized, higher quality 32K of Saturn assembler programming ever written, bar none. Everyone of the many incredibly gifted people involved in its creation loved what they they were doing, and it shows.

As many others, these are very well written words of yours, Valentim! If you allow me to, I second you. Thanks.

Luiz (Brazil)

Hello, Valentin --

I have downloaded the paper, and will examine it. I've been planning to withe a Forum article about using SOLVE and INTEG on RPN-based calc's, but wanted to understand Romberg a little more. This might help...

I also echo Luiz' compliment regarding your statement about the quality work embodied in HP calc's of the "golden era".

-- KS

i get -2 for test# 8.

also, the author should try sqrt(abs(x-1)) over [0,2]. what does the 71b math rom give? my 15c fails to return an answer after 300 seconds.

?

My emu71 returns -2

i get -2 for test# 8.

That's a typo in the document. The integrand is negative over the entire interior of the interval.

also, the author should try sqrt(abs(x-1)) over [0,2]. what does the 71b math rom give? my 15c fails to return an answer after 300 seconds.

The discontinuity in the 1st derivative at x = 1 will make life difficult for most numeric integrators. Trying this example on Free42 took 16,383 evaluations with ACC = 1e-6, i.e. a blink of an eye on a Pentium, but a lot longer on a Voyager with a 4-bit CPU whose clock speed is measured in kHz... (I estimate it will take almost 3 hours on a 15C.)


Splitting the integral into two parts, one over [0, 1], and the other over [1, 2], speeds things up a lot.

Edited: 7 Feb 2005, 7:22 a.m.