Leapfrog variants of iterative methods for linear algebraic equations
type: Item
instance of: scholarly article
title: Leapfrog variants of iterative methods for linear algebraic equations
zbMATH Open document ID: 0659.65026
DOI: 10.1016/0377-0427(88)90351-2
author: Paul E. Saylor
published in: Journal of Computational and Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let be \(x^{(i)}\) the sequence generated by an iterative method to solve the real or complex linear system \(Ax=b\). A leapfrog method is a variant such that \(x^{(i)}\) can be expressed directly in terms of \(x^{(i- 2)}\), and a grand-leap method expresses \(x^{(i)}\) directly by \(x^{(0)}\) without computation of intermediate iterates. These two methods are considered for Richardson's method, in particular for the Chebyshev case, and for a general second order method. Six different algorithms are presented and discussed, they include the calculation of the required parameters. The advantages of the methods concerning their efficiency on supercomputers are pointed out.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4078625
zbMATH Keywords: numerical examples
zbMATH Keywords: iterative method
zbMATH Keywords: leapfrog method
zbMATH Keywords: grand-leap method
zbMATH Keywords: Richardson's method
zbMATH Keywords: second order method
zbMATH Keywords: supercomputers
reviewed by: Lothar Berg
describes a project that uses: CHEBYCODE
MaRDI profile type: Publication
full work available at URL: 0377-0427(88)90351-2
OpenAlex ID: W1991633120
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description: scientific article; zbMATH DE number 4078625