Krylov methods for linear problems, eigenvalues, singular values and matrix functions
203 Stars
Updated Last
1 Year Ago
Started In
September 2017


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 License
CI license

Release notes for the latest version


This version requires at least Julia 1.6 because of new dependencies, namely on GPUArraysCore.jl to fix the GPU support, and on ChainRulesCore.jl to have AD support. In particular, this version comes with (experimental) AD support for linsolve. Future versions will extend this to eigsolve and potentially more.


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 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 1.0, the current stable 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.