29-Jun-2022 20:03:44

asa007_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 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
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.110223e-16

  Matrix order N = 2
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.440892e-16

  Matrix order N = 3
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.440892e-16

  Matrix order N = 4
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.464485e-15

  Matrix order N = 5
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.056162e-15

  Matrix order N = 6
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.209316e-15

  Matrix order N = 7
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.714528e-15

  Matrix order N = 8
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 5.301242e-15

  Matrix order N = 9
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 5.630775e-15

  Matrix order N = 10
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.762799e-15

  Matrix order N = 11
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.799269e-14

  Matrix order N = 12
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.001163e-14

  Matrix order N = 13
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.179324e-14

  Matrix order N = 14
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.379680e-14

  Matrix order N = 15
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.765606e-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
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 0.000000e+00

  Matrix order N = 2
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.280370e-16

  Matrix order N = 3
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.012679e-14

  Matrix order N = 4
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.481659e-13

  Matrix order N = 5
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.538677e-12

  Matrix order N = 6
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.262185e-10

  Matrix order N = 7
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.342947e-09

  Matrix order N = 8
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.070453e-07

  Matrix order N = 9
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.977940e-06

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

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

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

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

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

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

asa007_test():
  Normal end of execution.

29-Jun-2022 20:03:45