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Inner Product Free Krylov Methods for Large-Scale Inverse Problems

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arxiv 2409.05239 v1 pith:TYWBTNQP submitted 2024-09-08 math.NA cs.NA

Ariana N. Brown , Julianne Chung , James G. Nagy , Malena Sabaté Landman This is my paper · ORCID
classification math.NAcs.NA
keywords methodsinverselarge-scalelsluproblemsapproachfreehybrid
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In this study, we introduce two new Krylov subspace methods for solving rectangular large-scale linear inverse problems. The first approach is a modification of the Hessenberg iterative algorithm that is based off an LU factorization and is therefore referred to as the least squares LU (LSLU) method. The second approach incorporates Tikhonov regularization in an efficient manner; we call this the Hybrid LSLU method. Both methods are inner-product free, making them advantageous for high performance computing and mixed precision arithmetic. Theoretical findings and numerical results show that Hybrid LSLU can be effective in solving large-scale inverse problems and has comparable performance with existing iterative projection methods.

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  1. Randomized and Inner-product Free Krylov Methods for Large-scale Inverse Problems

    math.NA 2025-02 conditional novelty 6.0 of 10

    New inner-product-free Krylov methods, sCMRH and sLSLU, combine Hessenberg basis construction with randomized sketch-and-solve to produce residual norms close to minimal residual methods.

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