Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.
We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based...
The paper is concerned with the measurement of scalar physical quantities at nodes on the -dimensional unit sphere surface in the -dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider . We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful...
The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient...
AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...