Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

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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 languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 6th International Conference, NAA 2016
Subtitle of host publicationRevised Selected Papers
EditorsIvan Dimov, István Faragó, Lubin Vulkov
Place of PublicationCham
Number of pages9
ISBN (Print)9783319570983
Publication statusPublished - 2017
EventNAA 2016: 6th International Conference on Numerical Analysis and its Applications - Lozenetz, Bulgaria
Duration: 15 Jun 201622 Jun 2016
Conference number: 6

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10187 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceNAA 2016


  • Induced dimension reduction
  • Quadratic eigenvalue problem

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