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Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

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Numerical Analysis and Its Applications (NAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

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Abstract

In this work we are interested in the numerical solution of the Quadratic Eigenvalue Problem (QEP)

$$(\lambda ^2 M + \lambda D + K)\mathbf {x} = \mathbf {0},$$

where M, D, and K are given matrices of order N. Particularly, we study the applicability of the IDR(s) for eigenvalues to solve QEP. We present an IDR(s) algorithm that exploits the special block structure of the linealized QEP to compute its eigenpairs. To this end we incorporate ideas from Second Order Arnoldi method proposed in [3].

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References

  1. Arnoldi, W.E.: The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q. Appl. Math. 9, 17–29 (1951)

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  7. Sonneveld, P., van Gijzen, M.B.: IDR(\(s\)): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations. SIAM J. Sci. Comput. 31(2), 1035–1062 (2008)

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    R. Astudillo & M. B. van Gijzen

Authors
  1. R. Astudillo
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  2. M. B. van Gijzen
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Corresponding author

Correspondence to R. Astudillo .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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Astudillo, R., van Gijzen, M.B. (2017). Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_20

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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