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HP Forum Archive 16

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Sixth Order Linear Equation Solver for the hp 33s
Message #1 Posted by Palmer O. Hanson, Jr. on 16 Sept 2006, 10:55 p.m.

As part of a continuing effort to explore the capabilities of the hp 33s I have translated a sixth order linear equation solver for use on that machine. The documentation is much too long for a Forum topic so it has been entered as Article 676.

I believe that by judicious use of the statistics registers I should be able to fit a seventh order solver on the hp 33s but I haven't been able to push it through yet. I'm still working on it.

      
Re: Sixth Order Linear Equation Solver for the hp 33s
Message #2 Posted by ECL on 17 Sept 2006, 1:58 a.m.,
in response to message #1 by Palmer O. Hanson, Jr.

I'm very enthusiastic to give the program a try!

A lack of super-3x3 matrix support is the primary reason that my 33s has been in probation for the last 8 months.

Thanks, ECL

            
Expansion to seventh order
Message #3 Posted by Palmer O. Hanson, Jr. on 17 Sept 2006, 3:20 p.m.,
in response to message #2 by ECL

It turns out that it was not very difficult to expand the program to solve a seventh order set of linear equations. The changes required are:

1. Insert a CLSum command immediately after the CLVARS near the beginning of the program.

2. Add the following subroutine at the end of the program:

T0001 LBL T
T0002 STO i
T0003 x<>y
T0004 25
T0005 x>y?
T0006 RTN
T0007 3
T0008 STO+ i
T0009 RTN

3. Replace the STO i command with a XEQ T command at the following program locations:

B0003
B0009
C0006
D0006
D0014
E0006
F0005
F0012
F0020
G0003
G0007
G0011

The operating instructions are not changed.

For the test problem with a seventh order sub-Hilbert as the matrix A and all ones as the vector B the results are 

    Exact                hp 33s                Relative Error

       56               56.068858872            1.229E-03
    -1512            -1513.60579469             1.062E-03
    12600            12611.7867396              0.935E-03
   -46200           -46238.6331388              0.836E-03
    83160            83222.8860386              0.756E-03
   -72072           -72121.7495754              0.690E-03
    24024            24039.2548347              0.634E-03
for a mean relative error of 0.878E-03. For the same problem the HP-41 MathPac yields a mean relative error of 0.837E-02 and the ML-02 program for the TI-59 yields a mean relative error of 1.033E-04. In a subsequent submission I will provide comparisons with other machines and with other problems.
                  
Mea Culpa
Message #4 Posted by Palmer O. Hanson,Jr. on 18 Sept 2006, 10:27 a.m.,
in response to message #3 by Palmer O. Hanson, Jr.

The original sixth order program in Article 676 would run equally well in either RPN mode or ALG mode. My modification above of the program to provide a seventh order capability will run properly in ALG mode but will not run properly for all N when in RPN mode. To run properly in RPN mode the T subroutine must be modified by removing the x<>Y commsnd at T0003. The T subroutine for use in RPN mode then becomes:

T0001 LBL T
T0002 STO i
T0003 25
T0004 x>y?
T0005 RTN
T0006 3
T0007 STO+ i
T0008 RTN

      
Re: Sixth Order Linear Equation Solver for the hp 33s
Message #5 Posted by Gerson W. Barbosa on 17 Sept 2006, 7:38 p.m.,
in response to message #1 by Palmer O. Hanson, Jr.

That's really impressive! Now, a fourth or even a third order Complex Linear Equation Solver would be great, but that would be asking too much, I recognize :-)

One of the things that impressed me in my first decent programmable calculator, a TI-59 back in 1982, was its matrix abilities (ML-02 and ML-03). It would invert a 9x9 matrix in about 12 minutes!

Thanks for your continued efforts in writing and porting excellent software to the HP-33S.

Best regards,

Gerson W. Barbosa.

Edited: 17 Sept 2006, 7:39 p.m.

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