Solving parameterized generalized‎ ‎inverse eigenvalue problems via Golub-Kahan bidiagonalization

Document Type : Regular paper


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


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.


Volume 1, Issue 1 - Serial Number 1
January 2022
Pages 21-36
  • Receive Date: 13 December 2021
  • Revise Date: 29 December 2021
  • Accept Date: 31 December 2021
  • First Publish Date: 01 January 2022