consider the following consistent sylvester tensor equation[mathscr{x}times_1 a +mathscr{x}times_2 b+mathscr{x}times_3 c=mathscr{d},]where the matrices $a,b, c$ and the tensor $mathscr{d}$ are given and $mathscr{x}$ is the unknown tensor. the current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and ...

This paper presents equivalent forms of the Sylvester matrix equations. These equivalent forms allow us to use block linear methods for solving large Sylvester matrix equations. In each step of theses iterative methods we use global FOM or global GMRES algorithm for solving an auxiliary block matrix equations. Also, some numerical experiments for obtaining the numerical approximated solution of...

We present recursive blocked algorithms for solving triangular Sylvester-type matrix equations. Recursion leads to automatic blocking that is variable and \squarish". The main part of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We also present new highly optimized superscalar kernels for solving small-sized matrix equations stored in level 1 cach...

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...

For a generic n-degree polynomial system which contains n+1 polynomials in n variables, we give the construction of the generic mixed Cayley-Sylvester resultant matrix. There are n− 1 generic mixed Cayley-Sylvester resultant matrices between the classical Cayley resultant matrix and the classical Sylvester resultant matrix. The entries of these new resultant matrix are of degree m(1 < m < n + 1...

Abstract—A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order than that of the system matrix and furthermore, this small matrix can be chosen arbitraril...

This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Sylvester equation AX + XB = C by which we mean both A and B have positive diagonal entries and nonpositive off-diagonal entries and P = Im⊗A+B⊗ In is a nonsingular M -matrix, and C is entrywise nonnegative. It is proved that small relative perturbations to the e...