Testing Stefan's Matrix MultiTool Program for the HP35s Message #1 Posted by Palmer O. Hanson, Jr. on 17 Jan 2008, 10:30 p.m.
In a thread starting on of November 2, 2007 Stefan Vorkoetter announced that a Matrix MultiTool program for the HP35s was available at his site http://www.stefanv.com/calculators/hp35s_matrix_multitool.html . The only test results reported in the thread were for the determinant of a 6x6 Hilbert matrix and a modified 6x6 Hilbert where each term has been multiplied by 27720. This submission presents additional determinant calculations with both Stefan's program and with other machines. The exact determinants are provided followed by the calculated determinants and the relative errors of the calculated values. For each test case the results are listed in the order of decreasing relative error. The results show that Stefan's HP35s program yields determinants which are always very close to those obtained with another 12 digit machine such as the HP28S and are only bettered with machines which use more digits.
Modified 6x6 Hilbert where the multiplier is 27720:
Exact 2,435,091,120
HP35s 2,435,091,262.15 5.84E8
HP28S 2,435,091,046.63 3.01E8
TI85 2,435,091,108.7971 4.60E9
HP48G 2,435,091,119.56 1.81E10
Modified 7x7 Hilbert where the multiplier is 360360:
Exact 381,614,277,072,600
HP28S 381,615,844,742,xxx 7.06E5
HP35s 381,613,558,746,xxx 1.88E6
TI85 381,614,296,892,56x 5.19E8
Modified 8x8 Hilbert where the multiplier is 360360:
Exact 778,350,798,225
HP35s 777,765,489,858 7.52E4
HP28S 777,765,489,858 2.78E4
TI85 778,356,750,393.68 7.65E6
Modified 9x9 Hilbert where the multipler is 12,252,240 where the twelve digit "exact' value listed in the table is actually a rounded value from the exact determinant 6,048,061,401,328,975,508,480:
Exact 6.04806140133E21
HP35s 6.05382043333E21 9.52E4
TI85 6.05196898219E21 6.46E4
HP28S 6.04575974478E21 3.81E4
where I admit that I was surprised to find that the exact value for the 8x8 case was shorter than the exact value for the 7x7 case.
In early 2005 there was a series of threads comparing the calculated results from various machines for various tests. At one point Valentin Albillo expressed his dissatisfaction with tests using matrices made up of Hilberts, subHilberts and modifications since they involve matrices which have "... both very large elements and very small ones at the same time, i.e., very unbalanced, which is not a fair test ...". He proposed use of the following 7x7 matrix which has a determinant of exactly 1 and was designated as Albillo 1 :
58 71 67 36 35 19 60
50 71 71 56 45 20 52
64 40 84 50 51 43 69
31 28 41 54 31 18 33
45 23 46 38 50 43 50
41 10 28 17 33 41 46
66 72 71 38 40 27 69
Valentin commented that "... If you're aware that the matrix is difficult to begin with (like those nastylooking Hilbert matrices), you may be forewarned to extensively check the accuracy of the results you get. But if you happen to inadvertently stumble uponj such an 'innocent' looking matrix as this one, blindly trusting your results can result in cataatrophic failure. ..."
HP15C 1.080204421 8.02E2
HP71B 0.97095056196 2.91E2
HP28S 0.970960198039 2.91E2
HP35s 1.00282960115 2.83E3
CC40: 1.0028267103.. 2.83E3
TI95 1.0006767082.. 6.77E4
TI85 0.999646804338 3.52E4
HP48G 0.999945522778 5.45E5
In a subsequent submission I will present comparative results for matrix inversions and linear equations. You willl see that the Hp35s results are comparable to those obtained with the HP28S, but only if iterative refinement is not used with the HP28S. In the meantime if you want to see more of the April 2005 results you can go to directly to http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv015.cgi?read=72366
