In a thread starting on of November 2, 2007 Stefan Vorkoetter announced that a Matrix Multi-Tool program for the HP-35s 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 HP-35s program yields determinants which are always very close to those obtained with another 12 digit machine such as the HP-28S and are only bettered with machines which use more digits.

Modified 6x6 Hilbert where the multiplier is 27720:

Exact 2,435,091,120Modified 7x7 Hilbert where the multiplier is 360360:

HP-35s 2,435,091,262.15 5.84E-8

HP-28S 2,435,091,046.63 3.01E-8

TI-85 2,435,091,108.7971 4.60E-9

HP-48G 2,435,091,119.56 1.81E-10

Exact 381,614,277,072,600Modified 8x8 Hilbert where the multiplier is 360360:

HP-28S 381,615,844,742,xxx 7.06E-5

HP-35s 381,613,558,746,xxx 1.88E-6

TI-85 381,614,296,892,56x 5.19E-8

Exact 778,350,798,225Modified 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:

HP-35s 777,765,489,858 7.52E-4

HP-28S 777,765,489,858 2.78E-4

TI-85 778,356,750,393.68 7.65E-6

Exact 6.04806140133E21where 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.

HP-35s 6.05382043333E21 9.52E-4

TI-85 6.05196898219E21 6.46E-4

HP-28S 6.04575974478E21 3.81E-4

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, sub-Hilberts 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 60Valentin commented that "... If you're aware that the matrix is difficult to begin with (like those nasty-looking 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. ..."

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

HP-15C 1.080204421 8.02E-2In a subsequent submission I will present comparative results for matrix inversions and linear equations. You willl see that the Hp-35s results are comparable to those obtained with the HP-28S, but only if iterative refinement is not used with the HP-28S. In the meantime if you want to see more of the April 2005 results you can go to directly to http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=72366

HP-71B 0.97095056196 2.91E-2

HP-28S 0.970960198039 2.91E-2

HP-35s 1.00282960115 2.83E-3

CC-40: 1.0028267103.. 2.83E-3

TI-95 1.0006767082.. 6.77E-4

TI-85 0.999646804338 3.52E-4

HP-48G 0.999945522778 5.45E-5