LightKrylov: Lightweight implementation of Krylov subspace techniques in modern Fortran
Journal of Open Source Software
Abstract
Direct solvers for linear algebraic systems scale cubically in the problem’s dimension, rapidly becoming intractable for large-scale problems, while sparse factorization may still require quadratic storage du fill-in. Krylov techniques avoid these costs by needing only a routine that computes a matrix-vector product, iteratively building a subspace from which the solution is obtained. LightKrylov is a Fortran package providing a suite of such Krylov methods along with an easy-to-use high level API based on abstract types. It is primarily intended for applications where the linear operator of interest is only available implicitly via a matrix-vector subroutine and enables users to maximally re-use existing components of their code base (including parallelization), thus requiring a minimal set of changes without sacrificing computational performance.
Links
Published paper
Citation
@article{simon_kern2026,
author = {Simon Kern, J. and S. Frantz, Ricardo and Loiseau,
Jean-Christophe},
title = {LightKrylov: {Lightweight} Implementation of {Krylov}
Subspace Techniques in Modern {Fortran}},
journal = {Journal of Open Source Software},
volume = {11},
number = {117},
pages = {9623},
date = {2026-01-29},
url = {https://joss.theoj.org/papers/10.21105/joss.09623},
doi = {10.21105/joss.09623},
langid = {en}
}