INTERPRETATION AND IMPROVED SOLUTION APPROACH FOR ILL-CONDITIONED LINEAR-EQUATIONS

A simple method for obtaining physically realistic solutions to ill-conditioned or singular algebraic systems of linear equations is proposed and interpreted on both physical and mathematical grounds. Solutions obtained by this method are very close, and sometimes identical, to those obtained by the singular-value decomposition method, but are much simpler and more computationally efficient. The relationship of the method presented here, which we call epsilon-decomposition, to singular-value, Bayesian estimation and Levenberg-Marquardt methods for nonlinear parameter computations, is also presented. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.