Toward efficient polynomial preconditioning for GMRES

Loe, Jennifer A.; Morgan, Ronald B.

doi:10.1002/nla.2427

Title: Toward efficient polynomial preconditioning for GMRES

Journal Article · Thu Dec 30 00:00:00 EST 2021 · Numerical Linear Algebra with Applications

DOI:https://doi.org/10.1002/nla.2427· OSTI ID:1838187

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Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Baylor Univ., Waco, TX (United States)

Here, we present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many previous polynomial preconditioners. Our current implementation of this polynomial using its roots is naturally more stable than previous methods of computing the same polynomial. We implement further stability control using added roots, and this allows for high degree polynomials. We discuss the effectiveness and challenges of root-adding and give an additional check for stability. In this article, we study the polynomial preconditioner applied to GMRES; however it could be used with any Krylov solver. This polynomial preconditioning algorithm can dramatically improve convergence for some problems, especially for difficult problems, and can reduce dot products by an even greater margin.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: NA0003525; DMS-1418677

OSTI ID:: 1838187

Report Number(s):: SAND2021-16131J; 702364

Journal Information:: Numerical Linear Algebra with Applications, Vol. 29, Issue 4; ISSN 1070-5325

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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