Nonstationary two-stage multisplitting methods for symmetric positive definite matrices

AbstractNonstationary synchronous two-stage multisplitting methods for the solution of the symmetric positive definite linear system of equations are considered. The convergence properties of these methods are studied. Relaxed variants are also discussed. The main tool for the construction of the two-stage multisplitting and related theoretical investigation is the diagonally compensated reduction (cf. [1])

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Design and evaluation of tridiagonal solvers for vector and parallel computers

Postprint (published version

MULTISPLITTING PRECONDITIONERS BASED ON INCOMPLETE CHOLESKI FACTORIZATIONS

Let Ax = b be a linear system where A is a symmetric positive definite matrix. Preconditioners for the conjugate gradient method based on multisplittings obtained by incomplete Choleski factorizations of A are studied. The validity of these preconditioners when A is an M-matrix is proved and a parallel implementation is presented