RECSY is a library for solving triangular Sylvester-type matrix equations. Its objectives are both speed and reliability. In order to achieve these goals, RECSY is based on novel recursive blocked algorithms, which call high-performance kernels for solving small-sized leaf problems of the recursion tree. In contrast to explicit standard blocking techniques, our recursive approach leads to an au...

In this paper, by extending the well-known Jacobi and Gauss–Seidel iterations for Ax = b, we study iterative solutions of matrix equations AXB = F and generalized Sylvester matrix equations AXB + CXD = F (including the Sylvester equation AX + XB = F as a special case), and present a gradient based and a least-squares based iterative algorithms for the solution. It is proved that the iterative s...

and Applied Analysis 3 to a class of complex matrix equations with conjugate and transpose of the unknowns. Jonsson and Kågström 24, 25 proposed recursive block algorithms for solving the coupled Sylvester matrix equations and the generalized Sylvester and Lyapunov Matrix equations. Very recently, Huang et al. 26 presented a finite iterative algorithms for the one-sided and generalized coupled ...

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and  $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$  is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflex...

We present a new minimal residual method, called global R-linear GMRES, to solve the R-linear matrix equations X + AXB = C and X + AXB = C, where C, X ∈ Cm×n, X denotes the complex conjugate of X, X its complex conjugate transpose, and A, B are complex matrices with appropriate dimensions. We show that the new method requires fewer matrix-matrix products than the global GMRES method applied to ...

in this paper, we present gauss-sidel and successive over relaxation (sor) iterative methods for finding the approximate solution system of fuzzy sylvester equations (sfse), ax + xb = c, where a and b are two m*m crisp matrices, c is an m*m fuzzy matrix and x is an m*m unknown matrix. finally, the proposed iterative methods are illustrated by solving one example.

We present parallel algorithms for triangular periodic Sylvester-type matrix equations, conceptually being the third step of a periodic Bartels–Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the periodic Schur decomposition. The presented algorithms are designed and implemented in the framework of the recently developed HPC library SCASY a...

We continue our presentation of parallel ScaLAPACK-style algorithms for solving Sylvester-type matrix equations. In Part II, we present SCASY, a state-of-the-art HPC software library for solving 44 sign and transpose variants of eight common standard and generalized Sylvester-type matrix equations. The internal design of the library, Fortran interfaces and implementation issues are discussed in...

We present a survey of the results investigations one fields dealing with equivalence matrices originated by P. S. Kazimirs’kii and then continued developed his colleagues. formulate standard forms polynomial their finite sets respect to semiscalar generalized pairs over rings. Their applications development methods matrix factorization, solving equations, description structure solutions these ...