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.

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

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

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.

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