Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509867" target="_blank" >RIV/00216208:11320/25:10509867 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=o9147XT32E" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=o9147XT32E</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00366-025-02187-z" target="_blank" >10.1007/s00366-025-02187-z</a>

Result language

angličtina

Original language name

Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning

Original language description

Hardware trends have motivated the development of mixed precision algorithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive precision sparse matrix-vector produce routine, which may be used to accelerate the solution of sparse linear systems by iterative methods. This approach is also applicable to the application of inexact preconditioners, such as sparse approximate inverse preconditioners used in Krylov subspace methods. In this work, we develop an adaptive precision sparse approximate inverse preconditioner and demonstrate its use within a five-precision GMRES-based iterative refinement method. We call this algorithm variant BSPAI-GMRES-IR. We then analyze the conditions for the convergence of BSPAI-GMRES-IR, and determine settings under which BSPAI-GMRES-IR will produce similar backward and forward errors as the existing SPAI-GMRES-IR method, the latter of which does not use adaptive precision in preconditioning. Our numerical experiments show that this approach can potentially lead to a reduction in the cost of storing and applying sparse approximate inverse preconditioners, although a significant reduction in cost may comes at the expense of increasing the number of GMRES iterations required for convergence.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

20100 - Civil engineering

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Engineering with Computers

ISSN

0177-0667

e-ISSN

1435-5663

Volume of the periodical

41

Issue of the periodical within the volume

5

Country of publishing house

GB - UNITED KINGDOM

Number of pages

14

Pages from-to

3833-3846

UT code for WoS article

001550013100001

EID of the result in the Scopus database

2-s2.0-105013463215