Suppose that the first m Fourier coefficients of a piecewise analytic function are given. Direct expansion in a Fourier series suffers from the Gibbs phenomenon and lacks uniform convergence. Nonetheless, in this paper we show that, under very broad conditions, it is always possible to recover an n-term expansion in a different system of functions using only these coefficients. Such an expansio...

In this paper, we consider the issue of dual functions for the Bernstein basis which satisfy boundary conditions. The Jacobi weight function with the usual inner product in the Hilbert space are used. Some examples of the transformation matrices are given. Some figures for the weighted dual functions of the Bernstein basis with respect to the Jacobi weight function satisfying boundary condition...

Title ofprogram: TRIATOM Method of solution A basis is constructed as a product of radial (either Morse Catalogue number: AALO oscillator-like or spherical oscillator) functions and associated Legendre polynomials for the bending coordinate, with rotaProgram obtainable from: CPC Program Library, Queen’s Unition matrices carrying the rotational motion. A secular matrix versity of Belfast, N. Ire...

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gai...

The supersymmetry (SUSY) self–consistent approximation for the model of non–equilibrium thermodynamic system with quenched disorder is derived by making use of generalized second Legendre transformation. The equations for adiabatic and isothermal susceptibilities, memory and field induced parameters and the temperature of ergodicity breaking transition are obtained on the basis of asymptotic an...

A set of Fourier-like basis functions is constructed for Legendre–Galerkin method for non-periodic boundary value problems and a new space–time spectral method is proposed. A complete error analysis is carried out for a linear parabolic equation and numerical results are presented for several typical linear and nonlinear equations. © 2006 IMACS. Published by Elsevier B.V. All rights reserved. M...

We introduce a high-order time-domain discontinuous spectral element method for the study of the optical coupling by evanescent whispering gallery modes between two microcylinders, the building blocks of coupled resonator optical waveguide devices. By using the discontinuous spectral element method with a Dubiner orthogonal polynomial basis on triangles and a Legendre nodal orthogonal basis on ...

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

This paper introduces a new set of orthogonal moment Functions-franklin Moments (FMs). The kernel functions of FMs is Franklin set, which is a class of complete orthogonal spline function set of degree 1. The implementation of FMs does not involve any numerical approximation and has a rather low computation complexity, since the basis set has the advantages of lower order. These properties make...

Rotationally invariant moments constitute important techniques applicable to a versatile number of pattern recognition applications. Although the moments are invariant with regard to spatial transformations, in practice, due to the finite screen resolution, the spatial transformation themselves affect the invariance. This phenomenon jeopardizes the quality of pattern recognition. Therefore, thi...