Ten years of ABS methods: A review of theoretical results and computational achievements
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)].
scientific article; zbMATH DE number 438482