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]; Szyld, Daniel B.  ^[3]

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1. Georgia Inst. of Technology, Atlanta, GA (United States)
2. Univ. of Wuppertal (Germany)
3. 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.

• Research Organization: Temple Univ., Philadelphia, PA (United States); Georgia Institute of Technology, Atlanta, GA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0016578; SC0016564
• OSTI ID: 1832741
• Journal Information: Numerical Algorithms, Vol. 87, Issue 4; ISSN 1017-1398
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Asynchronous iterations
Parallel computing
Second order Richardson method