| Algorithm | Matrix types | External Package* |
Parallel |
Complex |
||
| Preconditioners | Jacobi | aij,baij,sbaij,dense | --- | X | X | |
| point block Jacobi | baij, bs = 2,3,4,5 | X | X | |||
| SOR | seqdense,seqaij,seqsbaij, mpiaij** |
--- | X | |||
| point block SOR*** | seqbaij, bs = 2,3,4,5 | X | ||||
| block Jacobi | aij,baij,sbaij | --- | X | X | ||
| additive Schwarz | aij,baij,sbaij | --- | X | X | ||
| Incomplete factorizations | ILU(k) | seqaij,seqbaij | --- | X | ||
| ICC(k) | seqaij,seqbaij | --- | X | |||
| ILU dt | seqaij | Sparsekit | ||||
| ILU(k) | aij | Euclid/hpypre (LLNL) | X | |||
| ILU dt | aij | Euclid/pilut (LLNL) | X | |||
| ILU(0)/ICC(0) | aij | BlockSolve95 | X | |||
| Matrix-free | infrastructure | X | X | |||
| Multigrid | infrastructure | X | X | |||
| geometric structured grid | X | X | ||||
| algebraic | aij | BoomerAMG/hypre (LLNL) | X | |||
| aij | ML/Trilinos (SNL) | X | ||||
| baij | Prometheus (LBNL) | X | ||||
| Approximate inverses | aij | Parasails/hypre (LLNL) | X | |||
| aij | SPAI | X | ||||
| Substructuring | balancing Neumann-Neumann | is | --- | X | X | |
| Direct solvers | LU | LU | seqaij,seqbaij | --- | X | |
| LU | seqaij | MATLAB | X | |||
| aij | Spooles | X | X | |||
| aij | PaStiX | X | X | |||
| aij | SuperLU (BNL) Sequential/Parallel | X | X | |||
| aij | MUMPS | X | X | |||
| seqaij | ESSL (IBM) | |||||
| seqaij | UMFPACK (U. Florida) | |||||
| seqaij | LUSOL | |||||
| dense | PLAPACK | X | X | |||
| Cholesky | Cholesky | seqaij,seqsbaij | --- | X | ||
| sbaij | Spooles | X | X | |||
| sbaij | PaStiX | X | X | |||
| sbaij | MUMPS | X | X | |||
| seqsbaij | DSCPACK (Penn State) | X | ||||
| dense | PLAPACK | X | X | |||
| QR | matlab | Matlab | ||||
| XXt and XYt | aij | --- | X | |||
| Krylov methods | Richardson | --- | X | X | ||
| Chebychev | --- | X | X | |||
| conjugate gradients | --- | X | X | |||
| GMRES | --- | X | X | |||
| Bi-CG-stab | --- | X | X | |||
| transpose free QMR | --- | X | X | |||
| conjugate residuals | --- | X | X | |||
| conjugate gradient squared | --- | X | X | |||
| bi-conjugate gradient | --- | X | X | |||
| MINRES | --- | X | X | |||
| flexible GMRES | --- | X | X | |||
| LSQR | --- | X | X | |||
| SYMMLQ | --- | X | X | |||
| LGMRES | --- | X | X | |||
| Conjugate gradient on the normal equations | --- | X | X |
*External Package If this column is filled in you must install the external package indicated to use this feature. See instructions
**A "block Jacobi" style SOR with lits local smoothing followed by update of ghost points from other processors, see MatRelax()
***Use PCType of PCSOR
This page was inspired by Jack Dongarra's freely available software for linear algebra list