Alexey Krylov

Krylov Subspaces

Many iterative methods for solving linear systems Ax = b and for finding eigenvalues and eigenvectors of a matrix A are based on the Krylov space 𝕂

Numerical Analysis and Scientific Computation by J. Leader


  1. Bouyghf, F., A unified approach to Krylov subspace methods for solving linear systems, Analysis of PDEs [math.AP]. Université du Littoral Côte d’Opale; Centre d’études doctorales en sciences et technologies (Rabat), 2023. English. ffNNT : 2023DUNK0664ff. fftel-04261470f
  2. Gleich, D.F., Krylov subspace approaches to solve linear systems, 2023, Purdue University.
  3. Gutknecht, M.H., A Brief Introduction to Krylov Space Methods for Solving Linear Systems, Zurich,
  4. Krylov, A. N. (1931). "О численном решении уравнения, которым в технических вопросах определяются частоты малых колебаний материальных систем" [On the Numerical Solution of Equation by Which are Determined in Technical Problems the Frequencies of Small Vibrations of Material Systems]. Izvestiia Akademii Nauk SSSR (in Russian). 7 (4): 491–539.
  5. Sogabe, T., Krylov Subspace Methods for Linear Systems: Principles of Algorithms, Springer, 2023. https://doi.org/10.1007/978-981-19-8532-4