Re: Even More Simultaneous Equation Solutions



#6

Hi all,

Okay then, I may have been somewhat "previous" in selling my 49G+ last year and replacing it with a TI84+SE as I have been having problems with the TI which are closely related to the problem discussed here. In short, Valentin's A-matrix cannot be effectively inverted in the TI as the lack of precision leads to the conclusion that the matrix is singular. :-(

I'll admit it here, I made a mistake! I will be sorting out monies for a new 49G+ shortly to tide me over until the OpenRPN project comes to fruition.

Tra

JasonG


#7

Jason:

The TI-83 Plus calculates the determinant of Valentin's matrix A to be zero which prevents doing an INV A * B solution on that machine.

The TI-85 calculates the determinant of Valentin's matrix A to be 9.90927530944e-08 which is within one per cent of the exact value of 1e-07. As indicated in the first submission in this thread the TI-85 gets respectable solutions for Valentin's problem whether using the INV A * B or Simultaneous Equation method.

What does the TI-84 find as the determinant of A?

In a thread in 2005 I presented results from calculation of determinants for 7x7 through 10x10 Hilbert matrices as follows:

                      7x7              8x8              9x9             10x10

TI-83+ 4.835795E-25 2.737004E-33 9.721266E-43 0
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

where the surprise was that the TI-83 Plus and TI-85 determinants for 7x7 through 9x9 were exactly the same and quite respectable but the TI-83 Plus determinant for the 10x10 Hilbert was zero. What does the TI-84 yield for those calculations?


#8

Well, my TI84+SE gives the determinant of A (where A is from the original system at the top of this thread) as zero. Not nearly zero but precisely zero. :-( It's a shame really as I quite like the TI84 in many ways, it's not a bad calculator. I suppose I'll have to dig out my 85 (if I can find it) and give that a go as I'm still unsure about the quality issues with the 49G+.

ttfn

Jason


#9

When I told TI-CARES about the zero for the determinant of the 10x10 Hilbert they responded with some words about the TI-83+ and TI-84 being less accurate machines and suggested that I should use the TI-86 or TI-89 for that kind of problem. That's not possible in my budget right now.

The TI-83+ doesn't get zero for the determinant of all 10x10 matrices. You might want to try Valentin's problem using RREF on the TI-84. On the TI-83+ and TI-85 I get

1.53301985311
0.999932803352
1.47525070084
1.47796598162
1.00032979830
0.522041369573
0
where the zero for the seventh element of the solution is truly curious. RREF on both machines solves some other seventh order systems satisfactorily.

#10

Yeah, I had spotted that. I guess it's because Valentin's problem is itself ill-conditioned, plus the method used is a little unstable (induced instability) so is bound to produce weird results. I agree that the zero is kinda odd though. :-)
I will be recovering my TI85 from its current hding place at the weekend, so I should be able to have a closer look at this problem then. :-)

ttfn

Jason


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