Items related to Abaffy Algorithms
Synopsis
The aim of this study is to present a new approach to the problems of solving linear systems of general form - determined, undetermined, over-determined, full rank or deficient rank - with a finite interactive process. The algorithms are given as particular members of a large class, containing two essential parameters whose structure is similar to the structure of the successful quasi-Newton algorithms for nonlinear optimization. Classical algorithms are reformulated, allowing derivation of new properties, and new algorithms discovered. The algorithms are also applied to nonlinear systems, where they generate a large class containing the Newton's method as a special case.
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