A block constant approximate inverse for preconditioning large linear systems

• Published in: SIAM journal on matrix analysis and applications Vol. 24; no. 3; pp. 822 - 851
• Main Authors: GUILLAUME, Ph, HUARD, A, LE CALVEZ, C
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 2003
• Subjects: Approximation; Boundary value problems; Exact sciences and technology; Integral equations; Iterative methods; Mathematical analysis; Mathematics; Methods; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Partial differential equations; Partial differential equations, boundary value problems; Sciences and techniques of general use; Sparsity; Multigrid method; Approximation; Linear system; Multigrid; Multipoles; Green function; Preconditioning; Multipole method; Inverse problem; Equation system
• ISSN: 0895-4798; 1095-7162
• DOI: 10.1137/S0895479802401515

A new class of approximate inverses is presented for preconditioning large linear systems issued from the discretization of elliptic boundary value problems. At the intersection of multipole, multigrid, and sparse approximate inverse (SAI) methods, they consist in approximating the inverse of a matrix by a block constant matrix instead of a sparse matrix like in SAI methods. They do not require more storage, or even less, and are well adapted to parallel computing, both for the construction of the preconditioner and for matrix-vector products. Numerical examples are provided and compared with SAI and incomplete Cholesky factorization preconditioners.