Newton's Method for Symmetric and Bisymmetric Solvents of the Nonlinear Matrix Equations

Abstract

Abstract. One of the interesting nonlinear matrix equations is the quadratic matrix equation defined bywhere X is a n × n unknown real matrix, and A, B and C are n × n given matrices with real elements. Another one is the matrix polynomialNewton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P (X). The method does not depend on the singularity of the Fréchet derivative. Finally, we give some numerical examples.