On Parameterised Quadratic Inverse Eigenvalue Problem

It is shown that if prescribed eigenvalues are distinct, then the parameterised quadratic inverse eigenvalue problem is equivalent to a multiparameter eigenvalue problem. Moreover, a sufficient condition for the problem solvability is established. In order to find approximate solution of this problem, we employ the Newton method based on the smooth QR-decomposition with column pivoting and prove its locally quadratic convergence. Numerical examples illustrate the effectiveness of the method. AMS subject classifications: 65F15 Key words: Quadratic inverse eigenvalue problem, multiparameter eigenvalue problem, smooth