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...

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of bor...

This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive preconditioned based on Kronecker product approximations A theoretical analysis shows that proposed converges an exact solution any initial at most finite steps in absence round-off errors. Compared with gradie...

This Thesis contains contributions in two different but closely related subfields of Scientific and Parallel Computing which arise in the context of various eigenvalue problems: periodic and parallel eigenvalue reordering and parallel algorithms for Sylvestertype matrix equations with applications in condition estimation. Many real world phenomena behave periodically, e.g., helicopter rotors, r...