Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0, 2π). Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to...

A simple way of obtaining multivariate wavelets is the tensor product of univariate wavelets. Multivariate wavelets are of interest in both theory and application. In this paper, we study the projection method, an inverse operation in some sense to the tensor product method, to investigate various properties of multivariate refinable function vectors and multivariate multiwavelets. To illustrat...

Abstract In this work, we study a global quadrature scheme for analytic functions on compact intervals based function values quasi-uniform grids of nodes. practice it is not always possible to sample at optimal nodes that give well-conditioned and quickly converging interpolatory rules the same time. Therefore, go beyond classical by lowering degree polynomial approximant applying auxiliary map...

The requirement that a Chebyshev quadrature formula have distinct real nodes is not always compatible with the requirement that the degree of precision of an npoint formula be at least equal to n. This condition may be expressed as | \d\ \p = 0, 1 g p, where d (dx, ■ ■ ■ , d„) with Mo(w) ~ , -IT dj = 2w A iM ; = 1, 2, • • ■ , z!, ZJ ,_, Pj(io), j = 0, 1, • • • , are the moments of the weight fu...