15-May-2025 16:38:21 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 = 8.707140 Before solving, X_ERROR = 1.424772 Before solving, X_ERROR = 1.424772 Before solving, X_ERROR = 16.189460 Before solving, X_ERROR = 20.685000 Before solving, X_ERROR = 22.183915 Before solving, X_ERROR = 20.685000 Before solving, X_ERROR = 16.189460 Before solving, X_ERROR = 8.707140 ITR = 1 Residual = 3.232138e+00 K = 1 Residual = 2.257515e+00 K = 2 Residual = 1.984659e+00 K = 3 Residual = 1.299707e+00 K = 4 Residual = 6.407423e-01 K = 5 Residual = 2.382088e-01 K = 6 Residual = 1.211012e-01 K = 7 Residual = 4.415716e-02 K = 8 Residual = 1.539490e-02 ITR = 2 Residual = 1.539490e-02 K = 1 Residual = 5.367263e-03 K = 2 Residual = 1.957067e-03 K = 3 Residual = 9.949386e-04 K = 4 Residual = 3.698883e-04 K = 5 Residual = 1.823512e-04 K = 6 Residual = 1.194176e-04 K = 7 Residual = 1.049841e-04 K = 8 Residual = 7.332703e-05 ITR = 3 Residual = 7.332703e-05 K = 1 Residual = 5.121589e-05 K = 2 Residual = 4.502565e-05 K = 3 Residual = 2.948624e-05 K = 4 Residual = 1.453642e-05 K = 5 Residual = 5.404206e-06 K = 6 Residual = 2.747403e-06 K = 7 Residual = 1.001787e-06 K = 8 Residual = 3.492618e-07 ITR = 4 Residual = 3.492618e-07 K = 1 Residual = 1.217663e-07 K = 2 Residual = 4.439968e-08 K = 3 Residual = 2.257202e-08 K = 4 Residual = 8.391599e-09 mgmres_st(): Iterations = 28 Final residual = 8.391599e-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. 15-May-2025 16:38:21