We consider computing the singular value decomposition of a bidiagonal matrix B. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accuracy, the singular values and singular vectors of B will be determined to much higher accuracy t...

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

Starting from optimal recovery (in the sense of Micchelli, Rivlin, and Winograd) of functions in reproducing kernel Hilbert spaces from function values at scattered data points, we show that any continuously embedded translation{invariant Hilbert subspace H of L 2 (IR d ) that allows continuous point evaluation is necessarily principal, i.e. it is the native space of a positive de nite function...

Applying nite-diierences to a generating function produces formulas for the permanent of a matrix. We present a setting of the nite-diierence parameters for which the permanent formula has many zero-valued terms when applied to 0-1 matrices. We outline a method to reduce computation by eliminating sets of zero-valued terms and show that the method signiicantly increases the computation speed.

We give a new and simple proof of a key lemma on the rank of a matrix in Leung's paper [3], where he showed there exists a family of nondeterministic nite automata fAng, with n states and exponential ambiguity, such that any smallest equivalent polynomially ambiguous nite automaton has 2 1 states. Keyword: nondeterministic automata, ambiguity, automata theory.

Voronoi cells and the notion of natural neighbours are used to develop a nite di erence method for the di usion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framewor...

We consider positive de nite and radial functions. After giving general results concerning the smoothness of general positive de nite and radial functions, we investigate the class of compactly supported, positive de nite, and radial functions, where every function consists of a univariate polynomial within its support. Especially, we show that these functions necessarily possess an even number...

in this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl‎. ‎308 (2000) 203-211] and [linear algebra appl‎. ‎428 (2008) 2177-2191]‎.

We study the Cholesky factorization of certain biinnnite matrices and related nite matrices. These results are applied to show that if the uniform translates of a suitably decaying multivariate function are orthonormali-zed by the Gram-Schmidt process over certain increasing nite sets, then the resulting functions converge to translates of a xed function which is obtained by a global orthonorma...