Skew-Symmetric Solvent for Solving a Polynomial Eigenvalue Problem

Abstract

Abstract. In this paper a nonlinear matrix equation is considered which has the formwhere X is an n × n unknown real matrix and A m , A m−1 , . . . , A 0 are n × n matrices with real elements. Newtons method is applied to find the skew-symmetric solvent of the matrix polynomial P (X). We also suggest an algorithm which converges the skew-symmetric solvent even if the Fréchet derivative of P (X) is singular.