MGMRES: A generalization of GMRES for solving large sparse nonsymmetric linear systems

Technical Report · Thu Oct 31 23:00:00 EST 1996

DOI:https://doi.org/10.2172/409863· OSTI ID:409863

Young, D M; Chen, Jen Yuan

This paper is concerned with the solution of the linear system Au = b, where A is a real square nonsingular matrix which is large, sparse and nonsymmetric. We consider the use of Krylov subspace methods. We first choose an initial approximation u{sup (0)} to the solution {bar u} = A{sup -1}b. The GMRES (Generalized Minimum Residual Algorithm for Solving Non Symmetric Linear Systems) method was developed by Saad and Schultz (1986) and used extensively for many years, for sparse systems. This paper considers a generalization of GMRES; it is similar to GMRES except that we let Z = A{sup T}Y, where Y is a nonsingular matrix which is symmetric but not necessarily SPD.

• Research Organization: Texas Univ., Austin, TX (United States). Center for Numerical Analysis
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: FG03-93ER25183
• OSTI ID: 409863
• Report Number(s): DOE/ER/25183--T2; ON: DE97000849
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
MATHEMATICS