30-Nov-2022 08:21:10

asa007_test():
  MATLAB/Octave version 4.2.2
  Test asa007().

asa007_test01():
  syminv() computes the inverse of a positive
  definite symmetric matrix.
  A compressed storage format is used.

  Here we look at the matrix A which is
  N+1 on the diagonal and
  N   on the off diagonals.

  Matrix order N = 1
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.110223e-16

  Matrix order N = 2
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.577567e-16

  Matrix order N = 3
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.475452e-16

  Matrix order N = 4
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.395529e-15

  Matrix order N = 5
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.202813e-15

  Matrix order N = 6
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.190054e-15

  Matrix order N = 7
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.828194e-15

  Matrix order N = 8
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 5.031823e-15

  Matrix order N = 9
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.998566e-15

  Matrix order N = 10
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.478549e-15

  Matrix order N = 11
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.067972e-14

  Matrix order N = 12
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.122710e-14

  Matrix order N = 13
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.193867e-14

  Matrix order N = 14
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.421441e-14

  Matrix order N = 15
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.498578e-14

asa007_test02():
  syminv() computes the inverse of a positive
  definite symmetric matrix.
  A compressed storage format is used.

  Here we look at the Hilbert matrix
  A(I,J) = 1 / ( I + J - 1 )

  We expect errors to grow quickly with N.

  Matrix order N = 1
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 0.000000e+00

  Matrix order N = 2
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.937408e-16

  Matrix order N = 3
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.348525e-15

  Matrix order N = 4
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.487756e-13

  Matrix order N = 5
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.883375e-12

  Matrix order N = 6
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 8.382671e-11

  Matrix order N = 7
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.724707e-09

  Matrix order N = 8
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.610475e-07

  Matrix order N = 9
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.384682e-06

  Matrix order N = 10
  Matrix nullity NULLTY = 1
  RMS ( C * A - I ) = 1.408078e+01

  Matrix order N = 11
  Matrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.782687e+00

  Matrix order N = 12
  Matrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.925892e+00

  Matrix order N = 13
  Matrix nullity NULLTY = 1
  RMS ( C * A - I ) = 4.062417e+00

  Matrix order N = 14
  Matrix nullity NULLTY = 1
  RMS ( C * A - I ) = 4.193206e+00

  Matrix order N = 15
  Matrix nullity NULLTY = 1
  RMS ( C * A - I ) = 4.318995e+00

asa007_test():
  Normal end of execution.

30-Nov-2022 08:21:10