Institution: Stanford University, Department of Computer Science

Title: A generalized conjugate gradient method for nonsymmetric systems of linear equations

Author: Concus, Paul

Author: Golub, Gene H.

Date: January 1976

Abstract: We consider a generalized conjugate gradient method for solving systems of linear equations having nonsymmetric coefficient matrices with positive-definite symmetric part. The method is based on splitting the matrix into its symmetric and skew-symmetric parts, and then accelerating the associated iteration using conjugate gradients, which simplifies in this case, as only one of the two usual parameters is required. The method is most effective for cases in which the symmetric part of the matrix corresponds to an easily solvable system of equations. Convergence properties are discussed, as well as an application to the numerical solution of elliptic partial differential equations.

http://i.stanford.edu/pub/cstr/reports/cs/tr/76/535/CS-TR-76-535.pdf