An implementation of a parallel ScaLAPACK-style solver for the general Sylvester equation, op(A)X−Xop(B) = C, where op(A) denotes A or its transpose A , is presented. The parallel algorithm is based on explicit blocking of the Bartels-Stewart method. An initial transformation of the coefficient matrices A and B to Schur form leads to a reduced triangular matrix equation. We use different matrix...

This paper presents a version of the Bartels-Stewart algorithm for solving Sylvester and Lyapunov equations that utilizes Jordan-Schur form equation matrices. The is type Schur which contains additional information about Jordan structure corresponding matrix. can be used to solve more efficiently in some cases. A two-level implemented allows us find directly non-scalar blocks solution These hav...

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 ...

Several classes of structured matrices (e.g., the Hadamard-Sylvester matrices and the pseudo-noise matrices) are used in the design of error-correcting codes. In particular, the columns of matrices belonging to the above two matrix classes are often used as codewords. In this paper we show that the two above classes essentially coincide: the pseudo-noise matrices can be obtained from the Hadama...

A unified deflating subspace approach is presented for the solution of a large class of matrix equations, including Lyapunov, Sylvester, Riccati and also some higher order polynomial matrix equations including matrix m-th roots and matrix sector functions. A numerical method for the computation of the desired deflating subspace is presented that is based on adapted versions of the periodic QZ a...

The problem of solving approximate GCD of multivariate polynomials has been well studied in the computational literature because of its importance particularly in engineering application[2, 6, 7]. Numbers of algorithms have been proposed to give the approach such as approximate subresultant PRS and modular algorithm using SVD. Here we focus on EZ-GCD[3], another method based on Hensel Lifting. ...

Abstract For a linear matrix function f in $$X \in {\mathbb {R}}^{m\times n}$$ X ∈ R m × n we consider inhomogeneous equations $$f(X) = E$$ f ( <...

In this paper we identify a class of Quasi-Birth-and-Death (QBD) processes where the transitions to higher (resp. lower) levels are restricted to occur only from (resp. to) a subset of the phase space. These restrictions induce a specific structure in the R or G matrix of the QBD, which can be exploited to reduce the time required to compute these matrices. We show how this reduction can be ach...

This paper presents an indirect adaptive control scheme of continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the ...

In this paper, based on the inner-outer (IO) iteration framework [17], by introducing some tunable parameters, an SOR-type IO (SIO) method is proposed for solving Sylvester matrix equation and coupled Lyapunov equations (CLMEs) in discrete-time jump linear systems with Markovian transitions. Fisrtly, SIO algorithm discrete developed, its convergence property analyzed choices of parameters are a...