Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

Conference paper (2017)

Authors

R.A. Astudillo Rengifo Numerical Analysis - EEMCS
M.B. van Gijzen Numerical Analysis - EEMCS
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Induced dimension reduction Quadratic eigenvalue problem
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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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].