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A Switching Approach to Avoid Breakdown in Lanczos-Type Algorithms

Farooq, Muhammad and Salhi, Abdellah (2014) 'A Switching Approach to Avoid Breakdown in Lanczos-Type Algorithms.' Applied Mathematics & Information Sciences, 8 (5). pp. 2161-2169. ISSN 1935-0090

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Lanczos-type algorithms are well known for their inherent instability. They typically breakdown when relevant orthogonal polynomials do not exist. Current approaches to avoiding breakdown rely on jumping over the non-existent polynomials to resume computation. This jumping strategy may have to be used many times during the solution process. We suggest an alternative to jumping which consists in switching between different algorithms that have been generated using different recurrence relations between orthogonal polynomials. This approach can be implemented as three different strategies: ST1, ST2, and ST3.We shall briefly recall how Lanczos-type algorithms are derived. Four of the most prominent such algorithms namely A4, A12, A5/B10 and A5/B8 will be presented and then deployed in the switching framework. In this paper, only strategy ST2 will be investigated. Numerical results will be presented. © 2014 NSP Natural Sciences Publishing Cor.

Item Type: Article
Uncontrolled Keywords: Lanczos algorithm; Systems of Linear Equations (SLE's); Formal Orthogonal Polynomials (FOP's); Switching; Restarting; Breakdown
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 12 Nov 2014 14:17
Last Modified: 12 Apr 2022 16:33

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