The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with a Sylvester matrix. In this paper, we present an algorithm based on fast Structured Total Least Norm(STLN) for constructing a Sylvester matrix of given lower rank and obtaining the nearest perturbed polynomials with exact GCD of given...

A relatively new branch of computational biology and chemistry has been emerging as an e ort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the structure of molecules, embedding them in Euclidean space, and nding the energetically favorable con gurations. We illustrate several e cient algebraic algorithms for enumerating all possible conformations ...

A direct method for eigenvalue reordering in a product of a K-periodic matrix sequence in periodic or extended periodic real Schur form is presented and analyzed. Each reordering of two adjacent sequences of diagonal blocks is performed tentatively to guarantee backward stability and involves solving a K-periodic Sylvester equation (PSE) and constructing a K-periodic sequence of orthogonal tran...

A direct method for eigenvalue reordering in a product of a K-periodic matrix sequence in periodic or extended periodic real Schur form is presented and analyzed. Each reordering of two adjacent sequences of diagonal blocks is performed tentatively to guarantee backward stability and involves solving a K-periodic Sylvester equation (PSE) and constructing a K-periodic sequence of orthogonal tran...

General parametric solution to a family of generalized Sylvester matrix equations arising in linear system theory is presented by using the socalled generalized Sylvester mapping which has some elegant properties. The solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution. The results provide great c...

In this paper, we propose the construction of two code generators for optical ZCZ codes of Zcz = 4n−2 with positive n and Zcz = 1 using the Sylvester-type Hadamard matrix, which are called ROM-type and non ROM-type code generators. The optical ZCZ code is a set of pairs of binary and bi-phase sequences with zero correlation zone. An optical code division multiple access (CDMA) system using opti...

In this paper we use the Riemann–Hilbert problem, with jumps supported on appropriate curves in complex plane, for matrix biorthogonal polynomials and apply it to find Sylvester systems of differential equations orthogonal its second kind functions as well. For aim, type Pearson weights are shown be instrumental. Several applications given, order increasing complexity. First, a general discussi...

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...

This article makes use of simultaneous decomposition four quaternion matrixes to investigate some Sylvester-like matrix equation systems. We present useful necessary and sufficient conditions for the consistency system equations in terms equivalence form block matrixes. also derive general solution according partition coefficient As an application system, we practical a ϕ-Hermitian provide when...

We consider linear time-invariant (LTI) systems of the following form Σ : { ẋ(t) = Ax(t) + Bu(t), t > 0, x(0) = x, y(t) = Cx(t) + Du(t), t ≥ 0, with stable state matrix A ∈ Rn×n and B ∈ Rn×m, C ∈ Rp×n, D ∈ Rp×m, arising, e.g., from the discretization and linearization of parabolic PDEs. Typically, in practical applications, we have a large state-space dimension n = O(105) and a small input and ...