On solving large sparse linear systems arising from linear programming

ISBN-13: 9783659763977 / Angielski / Miękka / 2018 / 128 str.

Venansius Baryamureeba; Trond Steihaug

Opis

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.

O autorze

Baryamureeba, Venansius
Professor Venansius Baryamureeba was born on 18th May 1969. He is a Professor of Computer Science. He served as the 14th Vice Chancellor of Makerere University. He has received several awards and recognitions including: Golden Jubilee Medal of the Republic of Uganda (the highest honour bestowed on a non-head of state by the President of Uganda.