A QUADRATICALLY CONVERGENT ALGORITHM FOR INVERSE EIGENVALUE PROBLEMS

Motivated by Kensuke Aishima's algorithm and Ulm's method, we propose a quadratically convergent algorithm for solving inverse eigenvalue problems. Compared with some existing algorithms, the proposed algorithm avoids solving (approximate) Jacobian equations and the Cayley transform. Thus, it seems more stable and needs less calculations. A quadratic convergence result is established under the condition that the relative generalized Jacobian matrix is nonsingular. Moreover, some numerical examples are given in the last section and comparisons with some known algorithms are made.