Abs Algorithms for Linear Equations and Abspack
نویسنده
چکیده
We present the main results obtained during a research on ABS methods in the framework of the project Analisi Numerica e Matematica Computazionale. 1. – The ABS algorithms. ABS algorithms were introduced by Abaffy, Broyden and Spedicato (1984), to solve linear equations first in the form of the basic ABS class, later generalized as the scaled ABS class and applied to linear least squares, nonlinear equations and optimization problems, see e.g. the monographs by Abaffy and Spedicato (1989) and Zhang, Xia and Feng (1999), or the bibliography by Nicolai and Spedicato (1997) listing over 300 ABS papers. In this paper we consider some new results obtained in the framework of project Analisi Numerica e Matematica Computazionale, including the performance of several codes of ABSPACK, a FORTRAN package under development. For later reference, we recall the scaled ABS algorithm for solving the following determined or underdetermined linear system, where rank(A) is arbitrary and A
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