The paper analyses various parallel incomplete factorizations based on the non-overlapping domain decomposition. The general framework is applied to the investigation of the preconditioning step in cg-like methods. Under certain conditions imposed on the nite element mesh, all matrix and vector types given by the special data distribution can be used in the matrix-by-vector multiplications. Not...

The paper presents a novel Newton method for constructing canonical Wiener-Hopf factorizations of complex matrix polynomials and spectral factorizations of positive definite matrix polynomials. The factorizations are the ones needed for discrete-time linear systems and hence with respect to the unit circle. The Jacobi matrix is analyzed, and the convergence of the method is proved and tested nu...

We formalize the notion of a factorization of a word, a so-called F -factorization, introduced in [7] when solving some open problems on word equations. We show that most of the factorizations considered in the literature t well into that framework, and in particular that central algorithmic problems, such as the uniqueness or the synchronizability, remain polynomial time solvable for an import...

The question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions. It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factoriz...

We study the factorizations of the permutation (1, 2, . . . , n) into k factors of given cycle types. Using representation theory, Jackson obtained for each k an elegant formula for counting these factorizations according to the number of cycles of each factor. In the cases k = 2, 3 Schaeffer and Vassilieva gave a combinatorial proof of Jackson’s formula, and Morales and Vassilieva obtained mor...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

A singular matrix A may have more than one LU factorizations. In this work the set of all LU factorizations of A is explicitly described when the lower triangular matrix L is nonsingular. To this purpose, a canonical form of A under left multiplication by unit lower triangular matrices is introduced. This canonical form allows us to characterize the matrices that have an LU factorization and to...

Two diierent factorizations of the Fibonacci innnite word were given independently in 10] and 6]. In a certain sense, these factorizations reveal a self-similarity property of the Fibonacci word. We rst describe the intimate links between these two factorizations. We then propose a generalization to characteristic sturmian words. R esum e. Deux factorisations du mot de Fibonacci ont et e donn e...