In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A ∈ Rn×n, B ∈ Rs×s, X and C ∈ Rn×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-SylvesterLike(GFSL) and Global GMRES-Sylvester-Like(GGSL) algorithms, respectively. Some theoretical results and ...

We provide necessary and sufficient conditions for the uniqueness of solution of the generalized Sylvester and ⋆-Sylvester equations, AXB − CXD = E and AXB+CX ⋆ D = E, respectively, where the matrix coefficients are allowed to be rectangular. These conditions generalize existing results for the same equations with square coefficients. Our characterization reveals unexpected constraints regardin...

A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterization in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of th...

A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...

The goal of this note is to give a presentation of a formal proof of the Sasaki-Murao algorithm [SM82]. This is an elegant algorithm for computing the determinant of a square matrix over an arbitrary commutative ring in polynomial time. Usual presentations of this algorithm are quite complex, and rely on some Sylvester identities [AL04]. We believe that the proof we shall present, which was obt...

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...

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 ...

This paper designs observers for matrix second-order linear systems on the basis of generalized eigenstructure assignment via unified parametric approach. It is shown that the problem is closely related with a type of so-called generalized matrix second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two unified complete ...

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...