This paper describes the application of the Sylvester resultant matrix to image deblurring. In particular, an image is represented as a bivariate polynomial and it is shown that operations on polynomials, specifically greatest common divisor (GCD) computations and polynomial divisions, enable the point spread function to be calculated and an image to be deblurred. The GCD computations are perfo...

This paper is concerned with the numerical solution of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated that the so called Cholesky factor ADI method with decent shift parameters can be very effective. In this paper we present a ...

If G and H are two cubic graphs, then we write H ≺ G, if G admits a proper edgecoloring f with edges of H , such that for each vertex x of G, there is a vertex y of H with f(∂G(x)) = ∂H(y). Let P and S be the Petersen graph and the Sylvester graph, respectively. In this paper, we introduce the Sylvester coloring conjecture. Moreover, we show that if G is a connected bridgeless cubic graph with ...

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 ...