IterativeSolvers.jl is a Julia package that provides efficient iterative algorithms for solving large linear systems, eigenproblems, and singular value problems. Most of the methods can be used matrix-free.
For bug reports, feature requests and questions please submit an issue. If you're interested in contributing, please see the Contributing guide.
For more information on future methods have a look at the package roadmap.
When solving linear systems
| Method | When to use it |
|---|---|
| [Conjugate Gradients](@ref CG) | Best choice for symmetric, positive-definite matrices |
| [MINRES](@ref MINRES) | For symmetric, indefinite matrices |
| [GMRES](@ref GMRES) | For nonsymmetric matrices when a good [preconditioner](@ref Preconditioning) is available |
| [IDR(s)](@ref IDRs) | For nonsymmetric, strongly indefinite problems without a good preconditioner |
| [BiCGStab(l)](@ref BiCGStabl) | Otherwise for nonsymmetric problems |
We also offer [Chebyshev iteration](@ref Chebyshev) as an alternative to Conjugate Gradients when bounds on the spectrum are known.
Stationary methods like Jacobi, Gauss-Seidel, SOR and SSOR can be used as smoothers to reduce high-frequency components in the error in just a few iterations.
When solving least-squares problems we currently offer [LSMR](@ref LSMR) and [LSQR](@ref LSQR). LSMR generally converges more quickly than LSQR.
For the Singular Value Decomposition we offer [SVDL](@ref SVDL), which is the Golub-Kahan-Lanczos procedure.
For eigenvalue problems we have at this point just the [Power Method](@ref PowerMethod) and some convenience wrappers to do shift-and-invert.