Solving parameterized generalized‎ ‎inverse eigenvalue problems via Golub-Kahan bidiagonalization

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