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H.-J. Jung*, J.-W. Oh+ and I.-W. Lee*

*Department of Civil Engineering, KAIST, Taejon, Korea
+Department of Civil and Environmental Engineering, Hannam University, Taejon, Korea

doi:10.4203/ccp.59.10.1

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H.-J. Jung, J.-W. Oh, I.-W. Lee, "A Numerically Stable Subspace Iteration Method with Shift", in B.H.V. Topping, B. Kumar, (Editors), "Developments in Analysis and Design using Finite Element Methods", Civil-Comp Press, Edinburgh, UK, pp 241-248, 1999. doi:10.4203/ccp.59.10.1

Abstract

A numerically stable eigensolution method for structures is presented. The proposed method is developed by improving the well-known subspace iteration method with shift. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue cannot be used, resulting in slower convergence. In this paper, the above singularity problem has been solved by introducing side conditions without sacrifice of convergence. The proposed method is always nonsingular even if a shift is on a distinct eigenvalue or multiple ones. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of the above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered.

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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: 59 DEVELOPMENTS IN ANALYSIS AND DESIGN USING FINITE ELEMENT METHODS Edited by: B.H.V. Topping and B. Kumar Paper X.1 A Numerically Stable Subspace Iteration Method with Shift H.-J. Jung, J.-W. Oh+ and I.-W. Lee *Department of Civil Engineering, KAIST, Taejon, Korea +Department of Civil and Environmental Engineering, Hannam University, Taejon, Korea doi:10.4203/ccp.59.10.1 purchase the full-text of this paper Full Bibliographic Reference for this paper H.-J. Jung, J.-W. Oh, I.-W. Lee, "A Numerically Stable Subspace Iteration Method with Shift", in B.H.V. Topping, B. Kumar, (Editors), "Developments in Analysis and Design using Finite Element Methods", Civil-Comp Press, Edinburgh, UK, pp 241-248, 1999. doi:10.4203/ccp.59.10.1 Abstract A numerically stable eigensolution method for structures is presented. The proposed method is developed by improving the well-known subspace iteration method with shift. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue cannot be used, resulting in slower convergence. In this paper, the above singularity problem has been solved by introducing side conditions without sacrifice of convergence. The proposed method is always nonsingular even if a shift is on a distinct eigenvalue or multiple ones. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of the above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered. 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 £74 +P&P)
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