Ten years of ABS methods: A review of theoretical results and computational achievements
type: Item
instance of: scholarly article
title: Ten years of ABS methods: A review of theoretical results and computational achievements
zbMATH Open document ID: 0784.65021
author: E. Spedicato
published in: Surveys on Mathematics for Industry
publication date: 1993-12-14T00:00:00Z
review text: The author gives a survey on the research and application of the ABS methods. The ABS methods were originally developed for solving linear algebraic systems by \textit{J. Abbafy}, \textit{C. G. Broyden} and the author [Numer. Math. 45, 361-376 (1984; Zbl 0535.65009)]. It was later extended to nonlinear systems by \textit{J. Abaffy}, the reviewer and the author [ibid. 51, 429-439 (1987; Zbl 0609.65038)]. During the ten years of research many important applications of ABS methods such as linear least squares, optimization and sparse systems were investigated by several mathematicians. The number of published papers is over 200. Therefore the author is restricted to show some interesting and very promising results. The interested reader is left however to study the original papers a list of which is given in the paper. A theory of linear ABS methods can be found in the monograph by \textit{J. Abaffy} and the author [ABS projective algorithms: Mathematical techniques for linear and nonlinear algebraic equations (1989; Zbl 0691.65022)].
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 438482
zbMATH Keywords: research survey
zbMATH Keywords: ABS methods
zbMATH Keywords: linear least squares
zbMATH Keywords: sparse systems
reviewed by: Aurél Galántai
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 438482