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A new Lanczos-type algorithm for systems of linear equations

Farooq, M and Salhi, A (2015) 'A new Lanczos-type algorithm for systems of linear equations.' Journal of Prime Research in Mathematics, 10 (1). 104 - 119. ISSN 1817-3462

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Abstract

Lanczos-type algorithms are efficient and easy to imple-ment. Unfortunately they breakdown frequently and well before con-vergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal polynomials of low degree. In this paper, we consider a recurrence relation that has not been studied before and which involves a relatively higher degree polynomial. Interestingly, it leads to an algorithm that shows su-perior stability when compared to existing Lanczos-type algorithms. This new algorithm is derived and described. It is then compared to the best known algorithms of this type, namely A<inf>5</inf>/B<inf>10</inf>, A<inf>8</inf>/B<inf>10</inf>, as well as Arnoldi's algorithm, on a set of standard test problems. Numerical results are included.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 06 Dec 2016 11:37
Last Modified: 30 Jan 2019 16:19
URI: http://repository.essex.ac.uk/id/eprint/18358

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