Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

R. Astudillo; M.B. van Gijzen

doi:10.1007/978-3-319-57099-0_20

Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

^*Corresponding author for this work

Numerical Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

Abstract

In this work we are interested in the numerical solution of the Quadratic Eigenvalue Problem (QEP) (λ²M + λD + K)x = 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 lin-ealized QEP to compute its eigenpairs. To this end we incorporate ideas from Second Order Arnoldi method proposed in [3].

Original language	English
Title of host publication	Numerical Analysis and Its Applications - 6th International Conference, NAA 2016
Subtitle of host publication	Revised Selected Papers
Editors	Ivan Dimov, István Faragó, Lubin Vulkov
Place of Publication	Cham
Publisher	Springer
Pages	203-211
Number of pages	9
ISBN (Print)	9783319570983
DOIs	https://doi.org/10.1007/978-3-319-57099-0_20
Publication status	Published - 2017
Event	NAA 2016: 6th International Conference on Numerical Analysis and its Applications - Lozenetz, Bulgaria Duration: 15 Jun 2016 → 22 Jun 2016 Conference number: 6

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10187 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	NAA 2016
Country/Territory	Bulgaria
City	Lozenetz
Period	15/06/16 → 22/06/16

Keywords

Induced dimension reduction
Quadratic eigenvalue problem

Access to Document

10.1007/978-3-319-57099-0_20

Cite this

Astudillo, R., & van Gijzen, M. B. (2017). Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. In I. Dimov, I. Faragó, & L. Vulkov (Eds.), Numerical Analysis and Its Applications - 6th International Conference, NAA 2016: Revised Selected Papers (pp. 203-211). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10187 LNCS). Springer. https://doi.org/10.1007/978-3-319-57099-0_20

Astudillo, R. ; van Gijzen, M.B. / Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. Numerical Analysis and Its Applications - 6th International Conference, NAA 2016: Revised Selected Papers. editor / Ivan Dimov ; István Faragó ; Lubin Vulkov. Cham : Springer, 2017. pp. 203-211 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this work we are interested in the numerical solution of the Quadratic Eigenvalue Problem (QEP) (λ2M + λD + K)x = 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 lin-ealized QEP to compute its eigenpairs. To this end we incorporate ideas from Second Order Arnoldi method proposed in [3].",

keywords = "Induced dimension reduction, Quadratic eigenvalue problem",

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booktitle = "Numerical Analysis and Its Applications - 6th International Conference, NAA 2016",

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Astudillo, R & van Gijzen, MB 2017, Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. in I Dimov, I Faragó & L Vulkov (eds), Numerical Analysis and Its Applications - 6th International Conference, NAA 2016: Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10187 LNCS, Springer, Cham, pp. 203-211, NAA 2016, Lozenetz, Bulgaria, 15/06/16. https://doi.org/10.1007/978-3-319-57099-0_20

Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. / Astudillo, R.; van Gijzen, M.B.
Numerical Analysis and Its Applications - 6th International Conference, NAA 2016: Revised Selected Papers. ed. / Ivan Dimov; István Faragó; Lubin Vulkov. Cham: Springer, 2017. p. 203-211 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10187 LNCS).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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N2 - In this work we are interested in the numerical solution of the Quadratic Eigenvalue Problem (QEP) (λ2M + λD + K)x = 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 lin-ealized QEP to compute its eigenpairs. To this end we incorporate ideas from Second Order Arnoldi method proposed in [3].

AB - In this work we are interested in the numerical solution of the Quadratic Eigenvalue Problem (QEP) (λ2M + λD + K)x = 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 lin-ealized QEP to compute its eigenpairs. To this end we incorporate ideas from Second Order Arnoldi method proposed in [3].

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KW - Quadratic eigenvalue problem

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BT - Numerical Analysis and Its Applications - 6th International Conference, NAA 2016

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Astudillo R, van Gijzen MB. Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. In Dimov I, Faragó I, Vulkov L, editors, Numerical Analysis and Its Applications - 6th International Conference, NAA 2016: Revised Selected Papers. Cham: Springer. 2017. p. 203-211. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-57099-0_20

Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

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