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Abstract.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… (More)
We present a review and bibliography of the main results obtained during a research on ABS (Abaffy, Broyden, Spedicato) methods.
ABS methods are a large class of algorithms for solving continuous and integer linear algebraic equations, and nonlinear continuous algebraic equations, with applications to optimization. Recent work… (More)
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… (More)
The results of computational experiments with ABS algorithms for KKT linear systems are reported.
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… (More)
In this paper we present a class of ABS methods for solving the KT equations. We compare several methods in this class with the classical methods of Aasen and the method based upon the QR… (More)
(A) Let x1 ∈ R n be arbitrary and H1 ∈ R n,n be nonsingular arbitrary. Set i = 1. (B) Compute the residual ri = Axi − b. If ri = 0, then stop, xi solves the problem. Otherwise compute si = HiA T vi,… (More)