08-Oct-2025 10:19:08 mgmres_test(): MATLAB/Octave version 6.4.0 Test mgmres(). mgmres_test01(): Test mgmres_st() on the simple -1,2-1 matrix. Test 1 Matrix order N = 20 Inner iteration limit = 20 Outer iteration limit = 1 Initial X_ERROR = 5.357238e+01 ITR = 1 Residual = 2.100000e+01 K = 1 Residual = 9.391486e+00 K = 2 Residual = 5.612486e+00 K = 3 Residual = 3.834058e+00 K = 4 Residual = 2.831639e+00 K = 5 Residual = 2.201398e+00 K = 6 Residual = 1.774824e+00 K = 7 Residual = 1.470294e+00 K = 8 Residual = 1.243933e+00 K = 9 Residual = 1.070259e+00 K = 10 Residual = 9.335639e-01 K = 11 Residual = 8.236878e-01 K = 12 Residual = 7.337994e-01 K = 13 Residual = 6.591531e-01 K = 14 Residual = 5.963599e-01 K = 15 Residual = 5.429421e-01 K = 16 Residual = 4.970501e-01 K = 17 Residual = 4.572787e-01 K = 18 Residual = 4.225429e-01 K = 19 Residual = 3.919930e-01 K = 20 Residual = 0.000000e+00 mgmres_st(): Iterations = 20 Final residual = 0.000000e+00 Final X_ERROR = 4.201633e-14 Test 2 Matrix order N = 20 Inner iteration limit = 10 Outer iteration limit = 2 Initial X_ERROR = 5.357238e+01 ITR = 1 Residual = 2.100000e+01 K = 1 Residual = 9.391486e+00 K = 2 Residual = 5.612486e+00 K = 3 Residual = 3.834058e+00 K = 4 Residual = 2.831639e+00 K = 5 Residual = 2.201398e+00 K = 6 Residual = 1.774824e+00 K = 7 Residual = 1.470294e+00 K = 8 Residual = 1.243933e+00 K = 9 Residual = 1.070259e+00 K = 10 Residual = 9.335639e-01 ITR = 2 Residual = 9.335639e-01 K = 1 Residual = 8.707991e-01 K = 2 Residual = 8.052481e-01 K = 3 Residual = 7.382919e-01 K = 4 Residual = 6.714950e-01 K = 5 Residual = 6.065840e-01 K = 6 Residual = 5.454219e-01 K = 7 Residual = 4.899610e-01 K = 8 Residual = 4.421317e-01 K = 9 Residual = 4.036072e-01 K = 10 Residual = 3.524539e-01 mgmres_st(): Iterations = 20 Final residual = 3.524539e-01 Final X_ERROR = 1.221284e+01 Test 3 Matrix order N = 20 Inner iteration limit = 4 Outer iteration limit = 5 Initial X_ERROR = 5.357238e+01 ITR = 1 Residual = 2.100000e+01 K = 1 Residual = 9.391486e+00 K = 2 Residual = 5.612486e+00 K = 3 Residual = 3.834058e+00 K = 4 Residual = 2.831639e+00 ITR = 2 Residual = 2.831639e+00 K = 1 Residual = 2.422241e+00 K = 2 Residual = 1.996521e+00 K = 3 Residual = 1.600974e+00 K = 4 Residual = 1.288921e+00 ITR = 3 Residual = 1.288921e+00 K = 1 Residual = 1.168683e+00 K = 2 Residual = 1.066834e+00 K = 3 Residual = 9.492963e-01 K = 4 Residual = 8.519354e-01 ITR = 4 Residual = 8.519354e-01 K = 1 Residual = 7.921140e-01 K = 2 Residual = 7.402888e-01 K = 3 Residual = 6.929995e-01 K = 4 Residual = 6.454025e-01 ITR = 5 Residual = 6.454025e-01 K = 1 Residual = 6.124110e-01 K = 2 Residual = 5.845053e-01 K = 3 Residual = 5.527674e-01 K = 4 Residual = 5.225523e-01 mgmres_st(): Iterations = 20 Final residual = 5.225523e-01 Final X_ERROR = 2.172377e+01 mgmres_test02(): Test mgmres_st() on matrix that is not quite the -1,2,-1 matrix, of order N = 9 First try, set initial estimate zero. Before solving, X_ERROR = 16.583124 ITR = 1 Residual = 3.000000e+00 K = 1 Residual = 2.236068e+00 K = 2 Residual = 1.914854e+00 K = 3 Residual = 1.290994e+00 K = 4 Residual = 3.779645e-01 K = 5 Residual = 2.350650e-16 mgmres_st(): Iterations = 5 Final residual = 2.350650e-16 After solving, X_ERROR = 0.000000 Final solution estimate: 1 3.500000 2 1.000000 3 1.000000 4 6.000000 5 7.500000 6 8.000000 7 7.500000 8 6.000000 9 3.500000 Second try, set initial estimate random. Before solving, X_ERROR = 9.120477 Before solving, X_ERROR = 1.839311 Before solving, X_ERROR = 1.839311 Before solving, X_ERROR = 16.597684 Before solving, X_ERROR = 21.091779 Before solving, X_ERROR = 22.590333 Before solving, X_ERROR = 21.091779 Before solving, X_ERROR = 16.597684 Before solving, X_ERROR = 9.120477 ITR = 1 Residual = 3.232428e+00 K = 1 Residual = 2.288129e+00 K = 2 Residual = 1.832241e+00 K = 3 Residual = 1.345829e+00 K = 4 Residual = 5.990522e-01 K = 5 Residual = 2.930180e-01 K = 6 Residual = 1.690107e-01 K = 7 Residual = 7.868254e-02 K = 8 Residual = 2.489774e-02 ITR = 2 Residual = 2.489774e-02 K = 1 Residual = 7.878460e-03 K = 2 Residual = 3.667800e-03 K = 3 Residual = 2.115561e-03 K = 4 Residual = 1.034797e-03 K = 5 Residual = 4.606064e-04 K = 6 Residual = 3.383274e-04 K = 7 Residual = 2.709188e-04 K = 8 Residual = 1.917745e-04 ITR = 3 Residual = 1.917745e-04 K = 1 Residual = 1.357508e-04 K = 2 Residual = 1.087037e-04 K = 3 Residual = 7.984574e-05 K = 4 Residual = 3.554075e-05 K = 5 Residual = 1.738426e-05 K = 6 Residual = 1.002712e-05 K = 7 Residual = 4.668102e-06 K = 8 Residual = 1.477141e-06 ITR = 4 Residual = 1.477141e-06 K = 1 Residual = 4.674157e-07 K = 2 Residual = 2.176043e-07 K = 3 Residual = 1.255126e-07 K = 4 Residual = 6.139274e-08 K = 5 Residual = 2.732700e-08 K = 6 Residual = 2.007239e-08 K = 7 Residual = 1.607316e-08 K = 8 Residual = 1.137766e-08 ITR = 5 Residual = 1.137766e-08 K = 1 Residual = 8.053866e-09 mgmres_st(): Iterations = 33 Final residual = 8.053866e-09 After solving, X_ERROR = 8.789198 After solving, X_ERROR = 14.000000 After solving, X_ERROR = 14.000000 After solving, X_ERROR = 8.426150 After solving, X_ERROR = 11.011358 After solving, X_ERROR = 12.124356 After solving, X_ERROR = 11.011358 After solving, X_ERROR = 8.426150 After solving, X_ERROR = 8.789198 Final solution estimate: 1 3.500000 2 1.000000 3 1.000000 4 6.000000 5 7.500000 6 8.000000 7 7.500000 8 6.000000 9 3.500000 mgmres_test(): Normal end of execution. 08-Oct-2025 10:19:08