Rapport Année : 2025

A note on the partial convergence management for the solution of of symmetric linear systems with multiple right-hand sides

Résumé

We consider the solution of large sparse symmetric linear systems with multiple right-hand sides available simultaneously. Based on the partial convergence detection and management, described in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265-285] and the breakdown-free idea discussed in [BIT Numer. Math., 57 (2017), pp. 379-403], the block conjugate residual and block conjugate gradient methods with partial convergence management are proposed. It enable to select the directions to use for extending the search space from one iteration to the next by choosing the directions that contribute the most to the residual norms. We illustrate the numerical and computational benefits of these two novel block conjugate direction variants on a set of simple academic examples enabling reproducible experiments.
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hal-04922247 , version 1 (31-01-2025)

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  • HAL Id : hal-04922247 , version 1

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Luc Giraud, Yanfei Xiang. A note on the partial convergence management for the solution of of symmetric linear systems with multiple right-hand sides. RR-9574, Inria Centre at the University of Bordeaux. 2025. ⟨hal-04922247⟩
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