A parallel preconditioner is presented for the solution of general sparse linear systems of equations. A sparse approximate inverse is computed explicitly and then applied as a precondi-tioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application only requires a matrix-vector product. The sparsity pattern… (More)
We extend the theory of Multigrid methods developed for PDE, Toeplitz and related matrices to the Block Toeplitz case. Prolongations and restrictions are defined depending on the zeroes of the generating function of the Block Toeplitz matrix. On numerical examples we compare different choices for prolongations and restrictions.
Article history: Available online xxxx Keywords: Electronic structure calculations Eigenvalue and eigenvector computation Blocked Householder transformations Divide-and-conquer tridiagonal eigensolver Parallelization a b s t r a c t The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many… (More)
A new parallel preconditioner is presented for the solution of large, sparse, nonsymmetric linear systems of equations. A sparse approximate inverse is computed explicitly, and then applied as a precondi-tioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application only requires a matrix-vector product. The… (More)
In this paper we discuss Multigrid methods for Toeplitz matrices. Then the restriction and prolongation operator can be seen as projected Toeplitz matrices. Because of the intimate connection between such matrices and trigonometric series we can express the Multigrid algorithm in terms of the underlying functions with special zeroes. This shows how to… (More)
We present an efficient implementation of the Modified SParse Approximate Inverse (MSPAI) preconditioner. MSPAI generalizes the class of preconditioners based on Frobenius norm minimizations, the class of modified preconditioners such as MILU, as well as interface probing techniques in domain decomposition: it adds probing constraints to the basic SPAI… (More)