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

Ullah, Saif and Farooq, Muhammad and Salhi, Abdellah An alternative derivation of a new Lanczos-type algorithm for systems of linear equations. UNSPECIFIED. UNSPECIFIED.

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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)
Uncontrolled Keywords: math.NA, math.NA
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 12 Nov 2014 14:27
Last Modified: 04 Jul 2018 13:15
URI: http://repository.essex.ac.uk/id/eprint/11538

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