Two data sets of indefinite matrix: afiro: contributed by S. Benson, M=N=59, nz=225, ill-conditioned. golan: contributed by T. Munson, M=N=4303, nz=33157, cond. approx 1.e8. xxx_A.dat: matrix in ascii format xxx_b.dat: rhs in ascii format xxx_u.dat: true solution in ascii format (greated by Matlab dense solver) xxx: converted Petsc binary sparse format (see `~petsc/matrices/readme' for details) /mat/examples/tests/ex78.c: example on how to convert Matlab ascii format to Petsc binary form. /sles/examples/tests/ex25.c: example on loading binary data and solve the indefinite system sequential output of ex25.c ============================== 1. on data set afiro: ("-pc_type jacobi" fails for all the three ksp methods It is an "indefinite preconditioner") ========= -ksp_max_it 150 -ksp_rtol 1.e-10 -pc_type none: ---------------------------------------------- CG: Number of iterations = 150 Residual norm: 0.616078; Error norm: 1.78961. MINRES: Number of iterations = 150 Residual norm: 0.0969619; Error norm: 1.81172. SYMMLQ: Number of iterations = 150 Residual norm: 0.216997; Error norm: 1.66926. -ksp_max_it 70 -ksp_rtol 1.e-10 -pc_type jacobi -pc_jacobi_rowmax ---------------------------------------------------------------- CG: Number of iterations = 70 Residual norm: 0.0011258; Error norm: 0.000230106. MINRES: Number of iterations = 70 Residual norm: 3.39516e-05; Error norm: 0.470816. SYMMLQ: Number of iterations = 70 Residual norm: 0.00461956; Error norm: 0.00202006. =================== 2. on data set golan: (-pc_type jacobi fails as an "Indefinite preconditioner") ===================== -np 1: --------- -pc_type none: --------------- CG: Number of iterations = 10000 Residual norm 7.69948; Error norm 397.12. MINRES: Number of iterations = 10000 Residual norm 0.0212476; Error norm 390.082. SYMMLQ: Number of iterations = 10000 Residual norm 2.94641; Error norm 388.242. -pc_type jacobi -pc_jacobi_rowmax: ----------------------------------- CG: Number of iterations = 10000 Residual norm: 1.24166; Error norm: 3.0973. MINRES: Number of iterations = 10000 Residual norm: 0.00976014; Error norm: 236.398. SYMMLQ: Number of iterations = 10000 Residual norm: 0.132509; Error norm: 0.497156.