Normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial dif...
详细信息
Normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. Normalized explicit preconditioned conjugate gradient schemes in conjunction with normalized approximate inverse matrix techniques are presented for solving sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also derived. A Parallel Normalized Explicit Preconditioned Conjugate Gradient method for distributed memory systems, using message passing inter-face (MPI) Communication library, is also given along with theoretical estimates on speedups, efficiency and computationalcomplexity. Application of the proposed method on a three-dimensional boundary value problem is discussed and numerical results are given for uniprocessor and multicomputer systems. Copyright (c) 2005 John Wiley & Sons, Ltd.
Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear...
详细信息
Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. (C) 2004 Elsevier Ltd. All rights reserved.
Normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference method of partial differential equations in three space variables, are presented. Normali...
详细信息
Normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference method of partial differential equations in three space variables, are presented. Normalized implicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate factorization procedures are presented for the efficient solution of sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also given. Application of the proposed method on characteristic three dimensional boundary value problems is discussed and numerical results are given.
Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear...
详细信息
Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. (C) 2004 Elsevier Ltd. All rights reserved.
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