Imagine the following scenario. You are in your overpriced hotel room, reviewing your notes for an important presentation that you will be giving later in the day. The people next door have their television cranked to maximum volume. It is so loud that you can hear the dialogue as well as the gunfire and explosions; it is from Sylvester Stallone's movie Judge Dredd. Despite an earlier request t...

The task of determining the greatest common divisors (GCD) for several polynomials which arises in image compression, computer algebra and speech encoding can be formulated as a low rank approximation problem with Sylvester matrix. This paper demonstrates a method based on structured total least norm (STLN) algorithm for matrices with Sylvester structure. We demonstrate the algorithm to compute...

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...