Report Number: CS-TR-76-533
Institution: Stanford University, Department of Computer Science
Title: A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations
Author: Concus, Paul
Author: Golub, Gene H.
Author: O'Leary, Dianne Prost
Date: January 1976
Abstract: We consider a generalized conjugate gradient method for solving sparse, symmetric, positive-definite systems of linear equations, principally those arising from the discretization of boundary value problems for elliptic partial differential equations. The method is based on splitting off from the original coefficient matrix a symmetric, positive-definite one that corresponds to a more easily solvable system of equations, and then accelerating the associated iteration using conjugate gradients. Optimality and convergence properties are presented, and the relation to other methods is discussed. Several splittings for which the method seems particularly effective are also discussed, and for some, numerical examples are given.