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.