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approximate inverse banded matrix techniques

ENGINEERING COMPUTATIONS 1999年第2-3期16卷 337-346页

作者： Gravvanis, GA Tech Univ Crete Dept Elect & Comp Engn Athens Greece

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

关键词： approximate inverse matrix techniques banded matrix factorization preconditioning

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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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Explicit isomorphic iterative methods for solving arrow-type linear systems

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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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EXPLICIT PRECONDITIONED ITERATIVE METHODS FOR SOLVING LARGE UNSYMMETRIC FINITE-ELEMENT SYSTEMS

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COMPUTING 1995年第2期54卷 167-183页

作者： LIPITAKIS, EA GRAVVANIS, GA Department of Informatics Athens University of Economics and Business Athens Greece

A class of Generalized approximate inverse matrix (GAIM) techniques, based on the concept of LU-sparse factorization procedures, is introduced for computing explicitly approximate inverses of large sparse unsymmetric matrices of irregular structure, without inverting the decomposition factors. Explicit preconditioned iterative methods, in conjunction with modified forms of the GAIM techniques, are presented for solving numerically initial/boundary value problems on multiprocessor systems. Application of the new methods on linear boundary-value problems is discussed and numerical results are given.

关键词： approximate inverse matrix techniques EXPLICIT PRECONDITIONERS PARALLEL ITERATIVE METHODS UNSYMMETRIC FINITE ELEMENT SYSTEMS INITIAL/BOUNDARY-VALUE PROBLEMS

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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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Software rejuvenation for resource optimization based on explicit approximate inverse preconditioning

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期189卷 163-177页

作者： Koutras, Vasilis P. Platis, Agapios N. Gravvanis, George A. Univ Aegean Dept Financial & Management Engn GR-82100 Chios Greece Democritus Univ Thrace Sch Engn Dept Elect & Comp Engn GR-67100 Xanthi Greece

When software applications run continuously, error conditions are accumulated and the result is a degradation of the computer system or even a crash failure. This phenomenon has been reported as software aging. A proactive method in order to counteract this phenomenon is software rejuvenation. In this paper, two software rejuvenation techniques are presented in a computer system in which the amount of free memory is used in order to model the resource degradation of the system. Furthermore, the cost of each technique is determined and the two techniques are compared with respect to the total expected downtime cost of performing rejuvenation and one of them is proposed. In addition, useful results about the rates of performing rejuvenation are derived and finally an optimal rejuvenation policy is proposed for such a computer system. (c) 2006 Elsevier Inc. All rights reserved.

关键词： software rejuvenation continuous time Markov chain optimal rejuvenation policy downtime cost approximate inverse matrix techniques preconditioning

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Domain Decomposition-Finite Difference approximate inverse Preconditioned Schemes for Solving Fourth-Order Equations

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Journal of Mathematical Modelling and Algorithms 2002年第3期1卷 181-192页

作者： Gravvanis, George A. Department of Information and Communication Systems Engineering University of the Aegean GR 832 00 Karlovasi Samos Greece

A new class of explicit approximate inverse preconditioning is introduced for solving fourth-order equations, based on the 'coupled equation approach', by the domain decomposition method in conjunction with various finite difference approximation schemes. Explicit approximate inverse arrow-type matrix techniques, based on the concept of sparse L U-type factorization procedures, are introduced for computing a class of approximate inverses. Explicit preconditioned conjugate gradient-type schemes are presented for the efficient solution of linear systems. Applications of the method to a biharmonic problem are discussed and numerical results are given. © 2002 Kluwer Academic Publishers.

关键词： approximate factorization procedure approximate inverse matrix techniques biharmonic equations domain decomposition method finite difference method parallel iterative methods preconditioning

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