Computer Solution of Large Linear Systems [Hardcover]

This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Introductory Material
Gaussian elimination for general linear systems
Gaussian elimination for sparse linear systems
Fast solvers for separable PDEs
Classical iterative methods
The conjugate gradient and related methods
Krylov methods for non--symmetric systems
Preconditioning
Multigrid methods