LightKrylov: Lightweight implementation of Krylov subspace techniques in modern Fortran

Journal of Open Source Software

paper
Reviving the Fortran Linear Algebra ecosystem
Authors

J. Simon Kern

Ricardo S. Frantz

Jean-Christophe Loiseau

Published

January 29, 2026

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.

Citation

BibTeX 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}
}
For attribution, please cite this work as:
Simon Kern, J., Ricardo S. Frantz, and Jean-Christophe Loiseau. 2026. “LightKrylov: Lightweight Implementation of Krylov Subspace Techniques in Modern Fortran.” Journal of Open Source Software 11 (117): 9623. https://doi.org/10.21105/joss.09623.