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

AbstractA 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