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.