Pré-Publication, Document De Travail Année : 2025

Randomized Krylov-Schur eigensolver with deflation

Résumé

This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient operations in low-dimensional spaces, such as sketch-orthogonalization processes and stable reordering of Schur factorizations. It also includes a practical deflation technique for converged eigenpairs, enabling the computation of the eigenspace associated with a given part of the spectrum. Numerical experiments are provided to demonstrate the scalability and accuracy of the method.

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hal-05244382 , version 1 (08-09-2025)

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Jean-Guillaume de Damas, Laura Grigori. Randomized Krylov-Schur eigensolver with deflation. 2025. ⟨hal-05244382⟩
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