Solving inverse eigenvalue problems by a projected newton method
Veronika Scholtyssek · Numerical Functional Analysis and Optimization · 1996
The inverse eigenvalue problem for symmetric matrices (IEP) is formulated as a system of two matrix equations. For solving the system a variation of Newton's method is used which has been proposed by Fusco and Zecca [Calcolo XXIII (1986), pp. 285–303] for the simultaneous computation of eigenvalues and eigenvectors of a given symmetric matrix. an iteration step of this method consists of a Newton step followed by an orthonormalization with the consequence that each iterate satisfies one of the given equations. The method converges locally y quadratically to regular solutions. The algorithm and some numerical examples are presented. In addition, it is shown that the so called Method III proposed by Friedland, Nocedal, and Overton [SIAM J. Numer. Anal.,24 (1987), pp. 634–667] for solving IEP may be constructed similarly to the method presented here