An alternative derivation of a new Lanczos-type algorithm for systems of linear equations

Authors

  • Saifullah Department of Mathematics University of Peshawar Khyber Pakhtunkhwa, 25120, Pakistan.
  • Muhammad Farooq Department of Mathematics University of Peshawar Khyber Pakhtunkhwa, 25120, Pakistan.
  • Abdellah Salhi Department of Mathematical Sciences University of Essex, Wivenhoe Park Colchester, CO4 3SQ, UK.

Keywords:

Lanczos Algorithm, Systems of Linear Equations, Formal Orthogonal Polynomials

Abstract

Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we consider recurrence relation A12 for the choice Ui(x) = Pi(x), where Ui is an auxiliary family of polynomials of exact degree i. It leads to a Lanczos-type algorithm that shows superior stability when compared to existing Lanczos-type algorithms. The new algorithm is derived and described. It is then computationally compared to the most robust algorithms of this type, namely A12, A5/B10 and A8/B10, on the same test problems. Numerical results are included.

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Published

2013-12-31

Issue

Vol. 45 (2013)

Section

Articles

License

Copyright (c) 2013 Saifullah, Muhammad Farooq, Abdellah Salhi

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

An alternative derivation of a new Lanczos-type algorithm for systems of linear equations. (2013). Punjab University Journal of Mathematics, 45(1), 37-47. https://pujm.pu.edu.pk/index.php/pujm/article/view/13