We study the quadratic matrix equation X2 − EX − F = 0, where E is diagonal and F is an M -matrix. Quadratic matrix equations of this type arise in noisy Wiener–Hopf problems for Markov chains. The solution of practical interest is a particular M -matrix solution. The existence and uniqueness of M -matrix solutions and numerical methods for finding the desired M -matrix solution are discussed b...

An iterative algorithm is presented for solving the extended Sylvester-conjugate matrix equation. By this iterativemethod, the solvability of thematrix equation can be determined automatically. When the matrix equation is consistent, a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a mo...

In this paper a nonlinear matrix equation is considered. Perturbation estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical examples. MSC: 65F10; 15A24 keywords: nonlinear matrix equation, perturbation estimates

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...