Approximate Generalized Inverse Preconditioning Methods for Least Squares Problems

摘要: iv erative methods to solve least squares problems more efficiently. We especially focused on one kind of preconditioners, in which preconditioners are the approximate generalized inverses coefficient matrices problems. proposed two different approaches for how construct matrices: is based Minimal Residual method with steepest descend direction, and other Greville’s Method an old developed computing inverse rank-one update. And these we also discuss apply them Both theoretical issues practical implementation about preconditioning discussed this thesis. Our numerical tests showed that our performed competitively rank deficient ill-conditioned As example from real world, linear programming problems, where many large-scale sparse arise. robustness than Cholesky decomposition method.