Summary of Sparse Linear Solvers Available In PETSc¶
Preconditioners¶
| Algorithm | Associated Type | Matrix Types | External Packages | Parallel | Complex | |
|---|---|---|---|---|---|---|
| Generic | Jacobi | — | X | X | ||
| Point Block Jacobi | — | X | X | |||
| Block Jacobi | — | X | X | |||
| SOR | — | X | ||||
| Point Block SOR | 
 | — | X | |||
| Additive Schwarz | — | X | X | |||
| Deflation | All | — | X | X | ||
| Incomplete | ILU | — | X | |||
| ILU with drop tolerance | X | |||||
| Euclid/hypre ( | X | |||||
| ICholesky | — | X | ||||
| Matrix Free | Infrastructure | All | — | X | X | |
| Multigrid | Infrastructure | All | — | X | X | |
| Geometric | All | — | X | X | ||
| Smoothed Aggregation | — | X | X | |||
| Structured Geometric | X | |||||
| Classical Algebraic | X | |||||
| Domain Decomposition | X | X | ||||
| Physics-based Splitting | Relaxation & Schur Complement | — | X | X | ||
| Least Squares Commutator | 
 | — | X | X | ||
| Approximate Inverse | AIV | X | ||||
| Substructuring | Balancing Neumann-Neumann | — | X | X | ||
| Balancing Domain Decomposition | — | X | X | 
Direct Solvers¶
| Algorithm | Associated Type | Matrix Types | External Packages | Parallel | Complex | |
|---|---|---|---|---|---|---|
| Direct LU | LU | — | X | |||
| X | ||||||
| X | X | |||||
| X | X | |||||
| X | X | |||||
| X | ||||||
| X | ||||||
| X | ||||||
| X | X | |||||
| X | X | |||||
| Direct Cholesky | Cholesky | — | X | |||
| X | X | |||||
| X | X | |||||
| X | ||||||
| X | X | |||||
| X | ||||||
| Direct QR | QR | MATLAB | ||||
| XXt and XYt | — | X | 
Krylov Methods¶
| Algorithm | Associated Type | External Packages | Parallel | Complex | 
|---|---|---|---|---|
| Richardson | — | X | X | |
| Chebyshev | — | X | X | |
| GMRES | — | X | X | |
| Flexible GMRES | — | X | X | |
| LGMRES | — | X | X | |
| Conjugate Gradient | — | X | X | |
| Conjugate Gradient Squared | — | X | X | |
| Conjugate Gradient for Least Squares | — | X | X | |
| Conjugate Gradient on Normal Equations | — | X | X | |
| Bi-Conjugate Gradient | — | X | X | |
| Stabilized Bi-Conjugate Gradient | — | X | X | |
| Transpose-free QMR | — | X | X | |
| Conjugate Residual | — | X | X | |
| Generalized Conjugate Residual | — | X | X | |
| Generalized Conjugate Residual (with inner normalization and deflated restarts) | X | X | ||
| Minimum Residual | — | X | X | |
| LSQR | — | X | X | |
| SYMMLQ | — | X | X |