December 20th, 2007, 11:16 pm
QuoteOriginally posted by: AVtstill would like to hear about exactness of results, a rapid but false one is not worth muchthe determinants are quite huge, so the condition numbers are high, I get ~ 15000 with MapleWell, here's a small test in Mathematica using these 300 x 300 random matrices. I create them, invert them, and multiply the original by the inverse to get A, ideally a diagonal of 1's.Then, I check to see how many of resulting 90000 elements of have |elem| > eps (off-diagonal)or |elem - 1| > eps (diagonal)I took eps = 1.0 10^(-13). I did this for 20 trials. The Count is the number that exceed eps, if Count > 0.The Worst is the absolute value of the maximum offender (or Abs[1 - elem] for diagonal elems).Some trials have Count = 0 and so are not in the list. The results:Trial, Count, Worst-------------------------------------{3, 27240, 7.3 x 10^-13}, {4, 81288, 1.0 x 10^-11}, {5, 12057, 2.9 x 10^-13},{6, 9382, 3.4 x 10^-13},{8, 1, 1.1 x 10^-13}, {10, 4601, 2.6 x 10^-13}, {11, 5, 1.1 x 10 ^-13}, {16, 3, 1.2 x 10^-13}, {17, 7540, 3.2 x 10^-13}, {18, 6, 1.2 x 10^-13}, {19, 8, 1.1 x 10^^-13}, {20, 83261, 8.1 x 10^-12}