Asynchronous Richardson iterations: theory and practice

Chow, Edmond; Frommer, Andreas; Szyld, Daniel B.

doi:10.1007/s11075-020-01023-3

Asynchronous Richardson iterations: theory and practice

Journal Article · Sun Oct 18 00:00:00 EDT 2020 · Numerical Algorithms

DOI:https://doi.org/10.1007/s11075-020-01023-3· OSTI ID:1832741

Chow, Edmond ^[1]; Frommer, Andreas ^[2]; ^[3]

Georgia Inst. of Technology, Atlanta, GA (United States); Temple University
Univ. of Wuppertal (Germany)
Temple Univ., Philadelphia, PA (United States)

We consider asynchronous versions of the first- and second-order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be proven to give convergence of the asynchronous methods. This is the first such analysis for asynchronous second-order methods. We find that for the first-order method, the optimal parameter value for the synchronous case also gives an asynchronously convergent method. For the second-order method, the parameter ranges for which we can prove asynchronous convergence do not contain the optimal parameter values for the synchronous iteration. In practice, however, the asynchronous second-order iterations may still converge using the optimal parameter values, or parameter values close to the optimal ones, despite this result. We explore this behavior with a multithreaded parallel implementation of the asynchronous methods.

View Accepted Manuscript (DOE)

Research Organization:: Georgia Inst. of Technology, Atlanta, GA (United States); Temple Univ., Philadelphia, PA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0016564; SC0016578

OSTI ID:: 1832741

Journal Information:: Numerical Algorithms, Journal Name: Numerical Algorithms Journal Issue: 4 Vol. 87; ISSN 1017-1398

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Second order Richardson method

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