[Octave-bug-tracker] [bug #41454] Inaccurate/incorrect result for inverse of symmetric matrix

[Lachlan Andrew]

Follow-up Comment #2, bug #41454 (project octave):

I can reproduce the error, but get yet another set of answers


matrixSize =

   239   239

matrixRank =  239
matrixCond =    4.9337e+07
machineEps =    2.2204e-16
withBackslashEye =

   2.5171e-09   3.8788e-08

withInv =

   5.2161e-01   4.8754e-08

symmetryHs = 0
symmetryMyInv =    2.5151e-08
symmetryOctInv =  0.22344


However, note also that I get


norm (inv(octInv) - Hs)
ans =    1.0759e-07


Perhaps the problem is just much less well conditioned than the condition
number suggests.  I note that the top left 145x145 block is just the identity.
 I assume that makes the condition number very good, despite the complexity in
the remainder of the matrix.  (This is where I should learn some linear
algebra...  Could either of you tell me the definition of the condition
number?)

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