Finding the Skew-Symmetric Solvent to a Quadratic Matrix Equation

Abstract

Abstract. In this paper we consider the quadratic matrix equation which can be defined bywhere X is a n × n unknown real matrix; A, B and C are n × n given matrices with real elements. Newton's method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fréchet derivative is singular. Finally, we give some numerical examples.