NEWTONS METHOD FOR A GENERALIZED INVERSE EIGENVALUE PROBLEM

A kind of generalized inverse eigenvalue problem is proposed which inc ludes the additive, multiplicative and classical inverse eigenvalue pr oblems as special cases. Newton's method is applied, and a local conve rgence analysis is given for both the distinct and the multiple eigenv alue cases. When the multiple eigenvalues are present we show how to s tate the problem so that it is not over-determined, and discuss a Newt on-method for the modified problem. We also prove that the modified me thod retains quadratic convergence, and present some numerical experim ents to illustrate our results. (C) 1997 by John Wiley & Sons, Ltd.