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An Improvement on a Class of Fixed Point Iterative Methods for Solving Absolute Value Equations

  • Nafiseh Nasseri Shams and Fatemeh Panjeh Ali Beik ORCID logo EMAIL logo

Abstract

We consider a class of iterative methods based on block splitting (BBS) to solve absolute value equations A x - | x | = b . Recently, several works were devoted to deriving sufficient conditions for the convergence of iterative methods of this type under certain assumptions including ν := A - 1 < 1 . However, the BBS-type iterative methods tend to converge slowly when 𝜈 is very close to one (i.e., ν 1 ). In this paper, using an auxiliary matrix, we develop a new approach by first rewriting the main problem into a new equivalent block system having shifted ( 1 , 1 ) -block and then constructing a fixed point iteration. The exploited strategy can significantly improve the convergence speed of the BBS-type iterative methods when ν 1 . Numerical experiments are reported to demonstrate the superiority of the new modified iterative scheme over the existing original form of BBS-type methods in the literature.

MSC 2010: 65F10

Acknowledgements

The authors would like to thank anonymous referees for their careful reading of the manuscript and helpful suggestions.

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Received: 2022-01-14
Revised: 2022-03-11
Accepted: 2022-03-23
Published Online: 2022-05-26
Published in Print: 2022-07-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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