Residual bounds of the nonlinear matrix equation X + A*F(X)A = Q
Ivan P. Popchev, Vera Angelova · International Journal of Data Science · 2016
In this paper, we consider the nonlinear matrix equation X + A*F(X)A = Q and we derive norm-wise non-local residual bounds for the accuracy of the solution obtained by an iterative algorithm. The residual bounds are derived using the method of Lyapunov majorants and the techniques of the fixed point principle. Two particular cases of the equation are considered in details and explicit expressions of the norm-wise non-local residual bounds are obtained as well. Numerical examples for the two, considered in the paper different cases of the nonlinear matrix function F(X) are provided to demonstrate the efficiency of the bounds proposed.