Accurate solutions of M -matrix algebraic Riccati equations

摘要: This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M-matrix Algebraic Riccati Equations (MARE) $$XDX - AX XB + C = 0 $$ by which we mean following conformally partitioned matrix \left( \begin{array}{ll}B\, \, -D\\-C\, A\end{array}\right)$$ a nonsingular or irreducible singular M-matrix. It known that such MARE has unique minimal nonnegative solution $${\Phi}$$. proved small perturbations to entries A, B, C, D introduce changes Thus smaller $${\Phi}$$ do not suffer bigger errors than larger entries, unlike existing for (general) Equations. We then discuss some minor but crucial implementation three methods so they can be used compute as accurately input data deserve. Current study based on previous authors’ Sylvester equation D = 0.