For a given subspace, the q-Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the q-Rayleigh-Ritz method defines the q-Ritz values and the q-Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the...

We prove that for a generic measure preserving transformation T , the closed group generated by T is a continuous homomorphic image of a closed linear subspace of L0(λ,R), where λ is Lebesgue measure, and that the closed group generated by T contains an increasing sequence of finite dimensional toruses whose union is dense.

Given the samples {f(xj) : j ∈ J} of a function f belonging to a shift invariant subspace of Lp(IR), we give a fast reconstruction algorithm that allows the exact reconstruction of f , as long as the sampling set X = {xj : j ∈ J} is sufficiently dense.

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

All spaces in this paper are Tychonoff. A Wallman base on a space X is a normal separating ring of closed subsets of X (see Steiner, Duke Math. J. 35 (1968), 269-276). Let T be a compact space and £ a Wallman base on T. For XCZT, define £x = {Ar)X\AE£}. Theorem 1. If X is a dense subspace of T, then T = w£x iff cItAHclrB = 0 whenever A, S£& and AC\B = 0. Theorem 2. T = w£xfor each dense XCZT if...

We show that each power bounded operator with spectral radius equal to one on a reflexive Banach space has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant cone if 1 belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators. Fo...

Given the samples ff(x j) : j 2 J g of a function f belonging to a shift invariant subspace of L p (IR d), we give a fast reconstruction algorithm that allows the exact reconstruction of f , as long as the sampling set X = fx j : j 2 J g is suuciently dense.

Clustering high dimensional data is an emerging research field. Most clustering technique use distance measures to build clusters. In high dimensional spaces, traditional clustering algorithms suffers from a problem called “curse of dimensionality”. Subspace clustering groups similar objects embedded in subspace of full space. Recent approaches attempt to find clusters embedded in subspace of h...

We propose a new search algorithm for a special type of subspace clusters, called maximal 1-complete regions, from high dimensional binary valued datasets. Our algorithm is suitable for dense datasets, where the number of maximal 1-complete regions is much larger than the number of objects in the datasets. Unlike other algorithms that find clusters only in relatively dense subspaces, our algori...

Let X be a finite-dimensional normed space and let Y⊆X its proper linear subspace. The set of all minimal projections from to Y is convex subset the operators we can consider affine dimension. We establish several results on possible values this prove optimal upper bounds in terms dimensions Y. Moreover, improve these estimates polyhedral spaces for an open dense subspaces given As consequence,...