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Gy. Molnarka* and B. Torok#

*Department of Mathematics, Szechenyi Istvan College, Gyor, Hungary
#Department of Numerical Analysis, Eotvos Lorand University, Budapest, Hungary

doi:10.4203/ccp.38.7.3

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Gy. Molnarka, B. Torok, "Residual Elimination Algorithm and its Application to Domain Decomposition", in B.H.V. Topping, (Editor), "Advances in Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, pp 253-257, 1996. doi:10.4203/ccp.38.7.3

Abstract

This paper presents a new direct algorithm for solving linear systems of equations. The theoretical background arid analysis of the proposed residual elimination algorithm is given. The general form and an optimized version of the residual elimination algorithm are formulated. The complexity of the suggested algorithm is the same as that of the Gaussian elimination (n³/3 + O(n²) where n is the dimension of the problem). The numerical stability properties of the implemented algorithm and the Gaussian elimination are compared. The numerical experiments show that the residual elimination algorithm is competitive with the Gaussian elimination in precision. A parallel version of the domain decomposition method is formulated, which has some advantages over the Schur complement method in the simplicity of the algorithm and in the case of implementation on parallel computing systems.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 38 ADVANCES IN COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping Paper VII.3 Residual Elimination Algorithm and its Application to Domain Decomposition Gy. Molnarka* and B. Torok# *Department of Mathematics, Szechenyi Istvan College, Gyor, Hungary #Department of Numerical Analysis, Eotvos Lorand University, Budapest, Hungary doi:10.4203/ccp.38.7.3 purchase the full-text of this paper Full Bibliographic Reference for this paper Gy. Molnarka, B. Torok, "Residual Elimination Algorithm and its Application to Domain Decomposition", in B.H.V. Topping, (Editor), "Advances in Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, pp 253-257, 1996. doi:10.4203/ccp.38.7.3 Abstract This paper presents a new direct algorithm for solving linear systems of equations. The theoretical background arid analysis of the proposed residual elimination algorithm is given. The general form and an optimized version of the residual elimination algorithm are formulated. The complexity of the suggested algorithm is the same as that of the Gaussian elimination (n³/3 + O(n²) where n is the dimension of the problem). The numerical stability properties of the implemented algorithm and the Gaussian elimination are compared. The numerical experiments show that the residual elimination algorithm is competitive with the Gaussian elimination in precision. A parallel version of the domain decomposition method is formulated, which has some advantages over the Schur complement method in the simplicity of the algorithm and in the case of implementation on parallel computing systems. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £82 +P&P)
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