A parallel alternating direction implicit preconditioning method
type: Item
instance of: scholarly article
title: A parallel alternating direction implicit preconditioning method
zbMATH Open document ID: 0734.65027
DOI: 10.1016/0377-0427(91)90027-H
author: Hong Jiang
author: Yau shu Wong
published in: Journal of Computational and Applied Mathematics
publication date: 1991-01-01T00:00:00Z
review text: The fast convergence of the ADI method predestines it to be used as a preconditioner \(M_ k^{-1}\) if a certain number of k iterations are applied to determine an approximate solution of a system of linear equations with the matrix \(A=H+V.\) An algorithm is described to compute the preconditioner \(M_ k^{-1}\) in order to achieve the maximum degree of parallelism. If H and V can be represented in the tensor product form, it is possible to recast the given system of equations into one where the commutativity holds. For this case a highly efficient algorithm, equivalent to the tensor product generalized ADI method, is established. If proper chosen, distinct acceleration parameters are used, it is shown that the sequential computations can completely be avoided, and the desired high parallelism is achieved. Moreover, it is shown that the resulting preconditioner \(M_ k\) is positive definite and thus is applicable in connection with conjugate gradient methods.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 4215262
zbMATH Keywords: parallel alternating direction implicit preconditioning method
zbMATH Keywords: parallel computation
zbMATH Keywords: convergence
zbMATH Keywords: ADI method
zbMATH Keywords: algorithm
zbMATH Keywords: preconditioner
zbMATH Keywords: conjugate gradient methods
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4215262