An optimal linear estimation approach to solve systems of linear algebraic equations

摘要

A method for the solution of systems of linear algebraic equations is presented. It is derived using an approach based on linear estimation theory and is directly related to a generalization of Huang's method (1975) proposed by Abaffy and Spedicato (1984). Exploring the approach adopted, the paper presents properties complementary to those found in the literature. Among these is included a Potter's factorized form of the method. In terms of applications, the method is analyzed as an alternative tool to get pseudoinverses, the solution of a class of quadratic programming problems and of ill-conditioned linear systems where iterative schemes are necessary.