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 

Physicsbased Splitting 
Relaxation & Schur Complement 
— 
X 
X 

Least Squares Commutator 

— 
X 
X 

Approximate Inverse 
AIV 
X 

Substructuring 
Balancing NeumannNeumann 
— 
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 

BiConjugate Gradient 
— 
X 
X 

Stabilized BiConjugate Gradient 
— 
X 
X 

Transposefree 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 