Krylov methods for linear problems, eigenvalues, singular values and matrix functions



A Julia package collecting a number of Krylov-based algorithms for linear problems, singular value and eigenvalue problems and the application of functions of linear maps or operators to vectors.

Documentation Build Status

Release notes for the latest version


This version introduces (minimal) breaking changes, if you use KrylovKit.jl with custom vector types: KrylovKit.jl no longer depends on eltype(::YourCustomVector) and similar(::YourCustumVector, ::Type{<:Number}). Instead, KrylovKit.jl does now rely on Base.:*(::Number, ::YourCustomVector) to be defined as a means of creating new vectors, possibly with a different scalar type, so as to be able to represent this computation. Note that Base.similar(::YourCustomVector) (without the second argument) should still be defined to create uninitialized vectors of the same type as the one of the argument.

The motivation for this is that using eltype(::YourCustomVector) to represent its scalar type, was often not the compatible with the requirements for Base.eltype if your type also supports iteration or indexing.


KrylovKit.jl accepts general functions or callable objects as linear maps, and general Julia objects with vector like behavior (as defined in the docs) as vectors.

The high level interface of KrylovKit is provided by the following functions:

  • linsolve: solve linear systems
  • eigsolve: find a few eigenvalues and corresponding eigenvectors
  • geneigsolve: find a few generalized eigenvalues and corresponding vectors
  • svdsolve: find a few singular values and corresponding left and right singular vectors
  • exponentiate: apply the exponential of a linear map to a vector
  • expintegrator: exponential integrator for a linear non-homogeneous ODE, computes a linear combination of the so-called ϕⱼ functions which generalize ϕ₀(z) = exp(z).


KrylovKit.jl can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add KrylovKit

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("KrylovKit.jl")


  • STABLE - documentation of the most recently tagged version.
  • DEVEL - documentation of the in-development version.

Project Status

The package is tested against Julia 0.7, 1.0, 1.1 and the nightly builds of the Julia master branch on Linux, macOS, and Windows, 32- and 64-bit architecture and with 1 and 4 threads.

Questions and Contributions

Contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems.

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Last Touched

14 days ago


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