Combination of real and imaginary parts (CRI) method is an efficient for solving a class large sparse linear systems with complex symmetric positive semi-definite coefficient matrices. In this work we will extend CRI approach to determine the approximate solution Sylvester equation We show that new algorithm converges unconditionally unique exact matrix equation. end test scheme by some numeric...

Combination of real and imaginary parts (CRI) works well for solving complex symmetric linear systems. This paper develops a generalization CRI method to determine the solution Sylvester matrix equation. We show that this, regardless condition, converges At end we test new scheme by numerical example.

Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorit...