Sixth Order Linear Equation Solver for the hp 33s - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: Sixth Order Linear Equation Solver for the hp 33s (/thread-99843.html) Sixth Order Linear Equation Solver for the hp 33s - Palmer O. Hanson, Jr. - 09-16-2006 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 - ECL - 09-17-2006 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 - Palmer O. Hanson, Jr. - 09-17-2006 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. Re: Sixth Order Linear Equation Solver for the hp 33s - Gerson W. Barbosa - 09-17-2006 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. Mea Culpa - Palmer O. Hanson, Jr. - 09-18-2006 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