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K. Meerbergen, "Theory and Numerical Methods for Eigenvalue Problems", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 181-206, 2008. doi:10.4203/csets.18.7

Keywords: algebraic eigenvalue problems, generalised eigenvalue problem, quadratic eigenvalue problem, Lanczos method, Arnoldi method, spectral transformation.

Abstract

This chapter reviews the theory on the algebraic eigenvalue problem, and in particular, the theory on the linear definite generalised eigenvalue problem (stiffness-mass), and the quadratic eigenvalue problem (stiffness-damping-mass). Numerical methods are presented for solving large scale problems, where the focus is on Krylov methods: Lanczos and Arnoldi, and the spectral transformation. Important notions such as inertia and sparse LDL^T factorisation are also touched on. Examples are included to illustrate the theory, as well as a bibliographical note with references to techniques other than those discussed in this chapter.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Computational Science, Engineering & Technology Series ISSN 1759-3158 CSETS: 18 COMPUTATIONAL METHODS FOR ACOUSTICS PROBLEMS Edited by: F. Magoulès Chapter 7 Theory and Numerical Methods for Eigenvalue Problems K. Meerbergen K.U. Leuven, Department of Computer Science, Leuven, Belgium doi:10.4203/csets.18.7 purchase the full-text of this chapter Full Bibliographic Reference for this chapter K. Meerbergen, "Theory and Numerical Methods for Eigenvalue Problems", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 181-206, 2008. doi:10.4203/csets.18.7 Keywords: algebraic eigenvalue problems, generalised eigenvalue problem, quadratic eigenvalue problem, Lanczos method, Arnoldi method, spectral transformation. Abstract This chapter reviews the theory on the algebraic eigenvalue problem, and in particular, the theory on the linear definite generalised eigenvalue problem (stiffness-mass), and the quadratic eigenvalue problem (stiffness-damping-mass). Numerical methods are presented for solving large scale problems, where the focus is on Krylov methods: Lanczos and Arnoldi, and the spectral transformation. Important notions such as inertia and sparse LDL^T factorisation are also touched on. Examples are included to illustrate the theory, as well as a bibliographical note with references to techniques other than those discussed in this chapter. purchase the full-text of this chapter (price £25) go to the previous chapter go to the next chapter return to the table of contents return to the book description purchase this book (price £95 +P&P)
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