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Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

  • R. AstudilloEmail author
  • M. B. van Gijzen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

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].

Keywords

Quadratic Eigenvalue Problem Induced Dimension Reduction 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands

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