Abstract. We present new formulae for the “near” inverses of striped Sylvester and mosaic Sylvester matrices. The formulae assume computation over floating-point rather than exact arithmetic domains. The near inverses are expressed in terms of numerical Padé-Hermite systems and simultaneous Padé systems. These systems are approximants for the power series determined from the coefficients of the...

The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation  

The Sylvester-Gallai theorem asserts that every finite set S of points in two-dimensional Euclidean space includes two points, a and b, such that either there is no other point in S is on the line ab, or the line ab contains all the points in S. V. Chvátal extended the notion of lines to arbitrary metric spaces and made a conjecture that generalizes the Sylvester-Gallai theorem. In the present ...

We bring together several new results related to the classical Sylvester-Gallai Theorem and its recently noted sharp dual. In 1951 Dirac and Motzkin conjectured that a configuration of n not all collinear points must admit at least n/2 ordinary connecting lines. There are two known counterexamples, when n = 7 and n = 13. We provide a construction that yields both counterexamples and show that t...

where X ∈ M(n,m)(K), play a central role in many areas of applied mathematics and in particular in systems and control theory. It is well known that if K is an algebraically closed field then the matrix equation (1) possesses a unique solution if and only if the matrices A and B have no common eigenvalues (see [[3]] and [11]). In this work we give a brief survey of methods used to solve the (SM...

We give a new structure theorem for subresultants precising their gap structure and derive from it a new algorithm for computing them. If d is a bound on the degrees and τ a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d2) arithmetic operations and size of intermediate computations 2τ . The key idea is to precise the relations between the successive Sy...

This Thesis contains contributions in two different but closely related subfields of Scientific and Parallel Computing which arise in the context of various eigenvalue problems: periodic and parallel eigenvalue reordering and parallel algorithms for Sylvestertype matrix equations with applications in condition estimation. Many real world phenomena behave periodically, e.g., helicopter rotors, r...