Farooq, M and Salhi, A (2014) A New Lanczos-Type Algorithm for Systems of Linear Equations. Journal of Prime Research in Mathematics, 10 (1). pp. 104-119.
Farooq, M and Salhi, A (2014) A New Lanczos-Type Algorithm for Systems of Linear Equations. Journal of Prime Research in Mathematics, 10 (1). pp. 104-119.
Farooq, M and Salhi, A (2014) A New Lanczos-Type Algorithm for Systems of Linear Equations. Journal of Prime Research in Mathematics, 10 (1). pp. 104-119.
Abstract
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence 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 superior 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 A5/B10, A8/B10, as well as Arnoldi's algorithm, on a set of standard test problems. Numerical results are included.
Item Type: | Article |
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Additional Information: | arXiv admin note: text overlap with arXiv:1403.0326 |
Uncontrolled Keywords: | Lanczos algorithm; Arnoldi algorithm; Systems of Linear Equations; Formal Orthogonal Polynomials |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 06 Dec 2016 11:37 |
Last Modified: | 16 May 2024 16:56 |
URI: | http://repository.essex.ac.uk/id/eprint/18358 |
Available files
Filename: 08.pdf