I only raised it because it is so bad compared to everyone else I've
looked at, including mine. An original copy of my result and my
implementation code are available on request. Please note, I cannot
speak for others but I didn't take a Hilbert matrix into account in
writing mine.
Paul
PLJsAPL=: 0 : 0
80.9999531610822 ¯3239.99665986097 41579.9420943319
¯249479.578965133 810808.433035166 ¯1513508.76245454
1621616.2451529 ¯926637.713155974 218789.430959011
¯3239.99667368818 172799.763174579 ¯2494795.89900529
15966690.2071222 ¯54053889.1945398 103783451.186115
¯113513134.744105 65894238.5094722 ¯15752839.8286812
41579.9425036479 ¯2494795.91108115 38419849.2522369
¯256132286.350815 891889090.567644 ¯1748102418.55488
1942335832.29382 ¯1141617699.88458 275674708.595751
¯249479.582883114 15966690.3618727 ¯256132287.510015
1756335480.92061 ¯6243223179.83275 12430950040.9097
¯13984817837.5535 8302674292.97357 ¯2021614600.3302
810808.450415449 ¯54053889.9691135 891889098.317587
¯6243223204.79328 22544971251.5605 ¯45450659629.1162
51648474522.865 ¯30918813482.0781 7581054973.44456
¯1513508.80311881 103783453.123491 ¯1748102440.39083
12430950134.7588 ¯45450659786.3692 92554068055.4922
¯106051533619.168 63930593442.9569 ¯15768594736.8895
1621616.2969454 ¯113513137.31893 1942335863.28028
¯13984817987.4734 51648474857.9506 ¯106051533934.55
122367153478.811 ¯74205153752.1709 18396694252.0436
¯926637.747107004 65894240.2479428 ¯1141617721.69509
8302674405.58929 ¯30918813765.3446 63930593798.5238
¯74205153941.7251 45229808347.2382 ¯11263282403.1867
218789.439925196 ¯15752840.2978892 275674714.654419
¯2021614632.92992 7581055060.93416 ¯15768594860.4611
18396694339.8914 ¯11263282427.9574 2815820646.25489
)
DialogAPL=: 0 : 0
81.00000837 ¯3240.000441 41580.00571 ¯2.494800309E5
8.108100843E5 ¯1.513512123E6 1.621620094E6 ¯9.266400324E5
2.187900028E5
¯3240.000352 172800.0149 ¯2494800.132 1.596672026E7
¯5.405399896E7 1.037836745E8 ¯1.135133904E8 6.589439254E7
¯1.575287780E7
41580.0033 ¯2494800.068 38419919.12 ¯2.561327823E8
8.918909013E8 ¯1.748106101E9 1.942340048E9 ¯1.141620239E9
2.756753345E8
¯249480.0094 15966719.51 ¯256132777.2 1.756338956E9
¯6.243235864E9 1.243097584E10 ¯1.398484736E10 8.302692071E9
¯2.021618982E9
810809.9941 ¯54053995.43 891890869.5 ¯6.243235770E9
2.254501711E10 ¯4.545075286E10 5.164858121E10 ¯3.091887772E10
7.581070803E9
¯1513511.922 103783666.1 ¯1748106017 1.243097550E10
¯4.545075234E10 9.255425620E10 ¯1.060517489E11 6.393072306E10
¯1.576862667E10
1621619.848 ¯113513379.8 1942339933 ¯1.398484685E10
5.164858015E10 ¯1.060517480E11 1.223673983E11 ¯7.420530117E10
1.839673057E10
¯926639.8769 65894385.62 ¯1141620161 8.302691705E9
¯3.091887687E10 6.393072205E10 ¯7.420530065E10 4.522989667E10
¯1.126330416E10
218789.963 ¯15752875.99 275675313.6 ¯2.021618879E9
7.581070548E9 ¯1.576862633E10 1.839673034E10 ¯1.126330410E10
2.815825985E9
)
NARS2000=: 0 : 0
80.99994931 ¯3239.996392 41579.93755
¯249479.5464 810808.3137 ¯1513508.519
1621615.966 ¯926637.5448 218789.3894
¯3239.996409 172799.7447 ¯2494795.584 15966687.95
¯54053880.89 103783434.2
¯113513115.2 65894226.72 ¯15752836.92
41579.93807 ¯2494795.6 38419843.93 ¯256132248.1
891888949.5 ¯1748102130 1942335500
¯1141617499 275674658.9
¯249479.5515 15966688.15 ¯256132249.6 1756335208
¯6243222172 1.243094797E10
¯1.398481546E10 8302672851 ¯2021614244
810808.3362 ¯54053881.9 891888959.6 ¯6243222204
2.254496755E10 ¯4.545065203E10
5.164846577E10 ¯3.091880818E10 7581053660
¯1513508.571 103783436.7 ¯1748102158
1.243094809E10 ¯4.545065223E10 9.255405253E10
¯1.060515157E11 6.393058258E10 ¯1.576859205E10
1621616.032 ¯113513118.6 1942335540
¯1.398481565E10 5.164846618E10 ¯1.060515161E11
1.223671329E11 ¯7.420514126E10 1.839669115E10
¯926637.5882 65894228.96 ¯1141617527 8302672992
¯3.091880853E10 6.393058301E10
¯7.420514148E10 4.522980079E10 ¯1.126328053E10
218789.4008 ¯15752837.52 275674666.5 ¯2021614284
7581053766 ¯1.576859219E10
1.839669126E10 ¯1.126328056E10 2815820182
)
On Mon, Jun 18, 2012 at 4:11 PM, Roger Hui <[email protected]> wrote:
> Do not be alarmed! :-) The Hilbert matrix is notoriously ill-conditioned
> and attempts to invert it does go very bad very fast. This is not due to
> any deficiency in the algorithm or implementation but to the fact that
> 64-bit floats do not have sufficient precision to represent the answer.
>
> http://en.wikipedia.org/wiki/Hilbert_matrix
> http://www.jsoftware.com/papers/APLQA.htm#Hilbert_matrix
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