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arXiv · 2508.05400

Randomized Krylov-Schur eigensolver with deflation

Jean-Guillaume de Damas·Laura Grigori
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Abstract

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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BibTeXRIS

Jean-Guillaume de Damas, Laura Grigori. 2025-08-07. Randomized Krylov-Schur eigensolver with deflation. https://arxiv.org/abs/2508.05400

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