Description:
"This book is concerned with solving very large sets of linear equations, where each equation involves only a small number of variables. Many applications involve equations of this kind and they often need to be solved repeatedly as their entries change. Very special methods are needed to make these calculations feasible. The authors have been involved in designing special algorithms and writing codes to implement them for over 40 years. This book aims to describe in a clear and simple way those algorithms that have stood the test of time, as well as those that have been developed recently to enable the efficient solution of far larger systems and to take advantage hardware"--
Sparse matrices : storage schemes and simple operations -- Gaussian elimination for dense matrices : the algebraic problems -- Gaussian elimination for dense matrices : numerical considerations -- Gaussian elimination for sparse matrices : an introduction -- Reduction to block triangular form -- Local pivotal strategies for sparce matrices -- Ordering sparse matrices for band solution -- Ordering based on dissection -- Implementing Gaussian elimination without symbolic facorize -- Implementing Gaussian elimination with symbolic FACTORIZE -- Gaussian elimination using trees -- Graphs for symmetric and unsymmetric matrices -- The SOLVE phase -- Other sparsity-oriented issues