Ullah, Saif and Farooq, Muhammad and Salhi, Abdellah (2014) An alternative derivation of a new Lanczos-type algorithm for systems of linear equations. UNSPECIFIED. UNSPECIFIED.
Ullah, Saif and Farooq, Muhammad and Salhi, Abdellah (2014) An alternative derivation of a new Lanczos-type algorithm for systems of linear equations. UNSPECIFIED. UNSPECIFIED.
Ullah, Saif and Farooq, Muhammad and Salhi, Abdellah (2014) An alternative derivation of a new Lanczos-type algorithm for systems of linear equations. UNSPECIFIED. UNSPECIFIED.
Abstract
Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we consider recurrence relation $A_{12}$ for the choice $U_i(x)=P_i(x)$, where $U_i$ 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 $A_{12}$, $A_5/B_{10}$ and $A_8/B_{10}$, on the same test problems. Numerical results are included.
Item Type: | Monograph (UNSPECIFIED) |
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Uncontrolled Keywords: | math.NA |
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: | 12 Nov 2014 14:27 |
Last Modified: | 16 May 2024 16:56 |
URI: | http://repository.essex.ac.uk/id/eprint/11538 |
Available files
Filename: paper5_v45_2013.pdf