On solving large sparse linear systems arising from linear programming

This book in Computer Science is tailored towards solving the standard linear programming problem and the standard linear regression problem. First we p ose these problems as sequences of weighted linear systems We discuss a combination of a direct solver and an iterative solver for solving these sequences of weighted linear systems For this mixed solver approach a class of preconditioners based on low rank corrections is discussed and preconditioners constructed The choice of the low rank correction matrix is based on derived theoretical b ounds on the eigenvalues of the precondi toned matrix. In addition for linear programming we suggest a globally convergent in exact interior p oint algorithm Based on this algorithm we state a globally convergent mixed interior p oint algorithm that suits the class of preconditioners mentioned above. Furthermore for the case of linear regression we discuss another class of preconditioners based on downdating a constant factorized matrix at every iteration Also a new convex weighting function for linear regression is suggested and preconditioners based on this function discussed.