Computational Mathematics and Computer Modeling with Applications (CMCMA)

Solving parameterized generalized‎ ‎inverse eigenvalue problems via Golub-Kahan bidiagonalization

https://doi.org/10.52547/CMCMA.1.1.21
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 21-36
Computational Mathematics and Computer Modeling with Applications (CMCMA)

Document Type : Regular paper

Authors

Zeynab Dalvand 1
Mohammad Ebrahim Dastyar 2

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

Abstract
In this study, we present two two-step methods to solve parameterized generalized inverse eigenvalue problems that appear in diverse areas of computation and engineering applications.  At the first step,  we  transfer the inverse eigenvalue problem into a  system of nonlinear equations by using of the Golub-Kahan bidiagonalization. At the second step, we use Newton's and Quasi-Newton's  methods for the numerical solution of system of nonlinear equations. Finally, we present some numerical examples which show that our methods are applicable for solving the parameterized inverse eigenvalue problems.

Keywords

Parameterized generalized inverse eigenvalue problem
Golub-Kahan bidiagonalization
Nonlinear equations
Newton's method
  • Receive Date 13 December 2021
  • Revise Date 29 December 2021
  • Accept Date 31 December 2021

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