Title: Lanczos-type algorithms with embedded interpolation and extrapolation models for solving large-scale systems of linear equations

Authors: Maharani Maharani; Niken Larasati; Abdellah Salhi; Wali Mashwani Khan

Addresses: Department of Mathematics, University of Jenderal Soedirman, Purwokerto, Jawa Tengah, Indonesia ' Department of Mathematics, University of Jenderal Soedirman, Purwokerto, Jawa Tengah, Indonesia ' Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO43YS, UK ' Department of Mathematics, University of Science and Technology, Kohat, Pakistan

Abstract: The new approach to combating instability in Lanczos-type algorithms for large-scale problems is proposed. It is a modification of so called the embedded interpolation and extrapolation model in Lanczos-type algorithms (EIEMLA), which enables us to interpolate the sequence of vector solutions generated by a Lanczos-type algorithm entirely, without rearranging the position of the entries of the vector solutions. The numerical results show that the new approach performs more effectively than the EIEMLA. In fact, we extend this new approach on the use of a restarting framework to obtain the convergence of Lanczos algorithms accurately. This kind of restarting challenges other existing restarting strategies in Lanczos-type algorithms.

Keywords: Lanczos algorithm; interpolation; extrapolation; systems of linear equations; embedded interpolation and extrapolation model in Lanczos-type algorithms; EIEMLA; restarting strategy.

DOI: 10.1504/IJCSM.2019.103675

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.5, pp.429 - 442

Received: 13 Jun 2017
Accepted: 03 Aug 2017

Published online: 21 Nov 2019 *

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