Review of ABS projection algorithms by J. Abaffy and E. Spedicato

Abs Algorithms for Linear Equations and Abspack

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, nonli...

WZ factorization via Abay-Broyden-Spedicato algorithms

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as...

Se p 20 02 ABS Methods and ABSPACK for Linear Systems and Optimization , a Review

ABS methods are a large class of methods, based upon the Egervary rank reducing algebraic process, first introduced in 1984 by Abaffy, Broyden and Spedicato for solving linear algebraic systems, and later extended to nonlinear algebraic equations, to optimization problems and other fields; software based upon ABS methods is now under development. Current ABS literature consists of about 400 pap...

Abs Algorithms for Linear Systems and Optimization: a Review and a Bibliography

In this paper, we 1. The scaled ABS class. ABS methods have been introduced by Abaffy, Broyden and Spedicato (1984), in a paper where the solution of linear algebraic equations was considered via the so called ABS unscaled or basic class. That class was later generalized to the so called scaled ABS class and then applied also to the solution of linear least squares, nonlinear algebraic equation...

Biconjugate Decomposition Using ABS Algorithms