Block preconditioning for the conjugate gradient method

Journal Article · Tue Jan 01 00:00:00 EST 1985 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0906018· OSTI ID:6692002

Concus, P; Golub, G H; Meurant, G

Block preconditioning for the conjugate gradient method are investigated for solving positive definite block tridiagonal systems of linear equations arising from discretization of boundary value problems for elliptic partial differential equations. The preconditioning rest on the use of sparse approximate matrix inverses to generate incomplete block Cholesky factorizations. Carrying out of the factorizations can be guaranteed under suitable conditions. Numerical experiments on test problems for two dimensions indicate that a particularly attractive preconditioning, which uses special properties of tridiagonal matrix inverses, can be computationally more efficient for the same computer storage than other preconditionings, including the popular point incomplete Cholesky factorization. 22 references, 6 figures, 12 tables.

• Research Organization: Univ. of California, Berkeley, CA (United States)
• DOE Contract Number: AC03-76SF00098; AC03-76SF00515
• OSTI ID: 6692002
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Vol. 6:1
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATRICES
NUMERICAL SOLUTION
BOUNDARY-VALUE PROBLEMS
FACTORIZATION
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
657000* - Theoretical & Mathematical Physics