Weight splitting iteration methods to solve quadratic nonlinear matrix equation [formula omitted

Abstract

The quadratic nonlinear matrix equationQ(Y)=MY2+NY+P,occurs in many applications such as the Quasi-Birth-Death processes, pseudo-spectra for quadratic eigenvalue problems and the quadratic eigenvalue problems. In this work, we propose efficient parametric iterative methods for finding the solution of this quadratic matrix equation based on weight splitting (WS) on matrices M and N, separately. We show that the proposed methods converge to the solution of the quadratic nonlinear matrix equation under conditions. Every iteration in proposed methods requires the solution of one or two linear matrix equations. Finally, various numerical examples indicate that the obtained methods in terms of CPU time, accuracy and computational cost are superior to the famous methods.