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Explicit isomorphic iterative methods for solving arrow-type linear systems

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2000年第2期74卷 195-205页

作者： Gravvanis, GA Tech Univ Crete Dept Elect & Comp Engn GR-73100 Khania Crete Greece

A new class of approximate inverse arrow-type matrix techniques based on the concept of sparse approximate LU-type factorization procedures is introduced for computing explicitly approximate inverses without inverting the decomposition factors. Isomorphic methods in conjunction with explicit preconditioned schemes based on approximate inverse matrix techniques are presented for the efficient solution of arrow-type linear systems. Applications of the proposed method on linear systems is discussed and numerical results are given.

关键词： arrow-type matrix bordered diagonal matrix approximate factorization procedures approximate inverse matrix techniques isomorphic methods preconditioning iterative methods

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An approximate inverse matrix technique for arrowhead matrices

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1998年第1期70卷 35-45页

作者： Gravvanis, GA Nursing Mil Acad GR-16201 Athens Greece Tech Univ Crete Dept Elect & Comp Engn GR-73100 Khania Crete Greece

A new class of approximate inverse matrix techniques based on the concept of sparse LU-type factorization procedures is introduced for computing explicitly inverses of arrowhead matrices without inverting the decomposition factors, Explicit preconditioned iterative schemes in conjunction with AIM techniques are presented for the efficient solution of linear systems. Applications of the method on a linear system are discussed and numerical results are given.

关键词： arrowhead matrix bordered diagonal matrix approximate factorization procedures approximate inverse matrix techniques preconditioning

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Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2003年第1-3期45卷 263-272页

作者： Gravvanis, GA Athens Univ Econ & Business Dept Informat GR-10434 Athens Greece Univ Aegean Dept Math GR-83200 Karlovassi Samos Greece

A new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： arrow-type matrix domain decomposition approximate factorization procedures approximate inverse matrix techniques preconditioning parallel iterative methods

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Finite Element approximate Inverse Preconditioning for solving 3D Biharmonic Problems on Shared Memory Systems

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2011年第4期71卷 305-330页

作者： Gravvanis, G. A. Giannoutakis, K. M. Democritus Univ Thrace Sch Engn Dept Elect & Comp Engn GR-67100 Xanthi Greece Informat & Telemat Inst Ctr Res & Technol Hellas GR-57001 Thessaloniki Greece

In this paper we present parallel explicit approximate inverse matrix techniques for solving sparse linear systems on shared memory systems, which are derived using the finite element method for biharmonic equations in three space variables. Our approach for solving such equations is by considering the biharmonic equation as a "coupled equation approach" (pair of Poisson equation), using a FE approximation scheme, yielding an "inner-outer" iteration method. Additionally, parallel approximate inverse matrix algorithms are introduced for the efficient solution of sparse linear systems, based on an anti-diagonal computational approach that eliminates the data dependencies. Parallel explicit preconditioned conjugate gradient-type schemes in conjunction with parallel approximate inverse matrix algorithms are presented for the efficient solution of sparse linear systems. Theoretical estimates on computational complexity of the parallel explicit preconditioned conjugate gradient method along with theoretical speedups and efficiency are also presented. Applications of the proposed methods on characteristic biharmonic problems are discussed and numerical results are given.

关键词： Biharmonic equations finite element method sparse linear systems approximate factorization procedures parallel approximate inverse matrix algorithms parallel preconditioned conjugate gradient methods shared memory systems

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On the solution of boundary value problems by using fast generalized approximate inverse banded matrix techniques

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JOURNAL OF SUPERCOMPUTING 2003年第2期25卷 119-129页

作者： Gravvanis, GA Univ Aegean Dept Informat & Commun Syst Engn GR-83200 Karlovassi Samos Greece

A class of finite difference schemes in conjunction with approximate inverse banded matrix techniques based on the concept of LU-type factorization procedures is introduced for computing fast explicit approximate inverses. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of banded linear systems. A theorem on the rate of convergence and estimates of the computational complexity required to reduce the L-infinity-norm of the error is presented. Applications of the method on linear and non-linear systems are discussed and numerical results are given.

关键词： banded matrix approximate factorization procedures approximate inverse matrix techniques preconditioning parallel iterative methods rate of convergence computational complexity

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On the solution of boundary value problems by using fast generalized approximate inverse banded matrix techniques

On the solution of boundary value problems by using fast gen...

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International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA 2001)

作者： Gravvanis, GA Univ Aegean Dept Informat & Commun Syst Engn GR-83200 Karlovassi Samos Greece

关键词： banded matrix approximate factorization procedures approximate inverse matrix techniques preconditioning parallel iterative methods rate of convergence computational complexity

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