Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
type: Item
instance of: scholarly article
title: Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
zbMATH Open document ID: 1057.41003
author: Lilian Wang
author: Ben-Yu Guo
published in: Journal of Approximation Theory
publication date: 2004-08-10T00:00:00Z
review text: The paper is devoted to Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces. The approximation results are of the form \[ \left\| Q_N v-v \right\| _{B_1} \leq d_{N,\alpha,\beta}| v |_{B_2}, \] where \(B_1\) and \(B_2\) are non-uniformly Jacobi weighted Sobolev spaces, \(Q_N\) is an orthogonal projection upon the set of polynomials of degree at most \(N\), and \(d_{N,\alpha,\beta}\) is an explicit function of \(N\), \(\alpha\) and \(\beta\), independent of \(v\). The results are general and all estimates are as sharp as possible. First some basic results on Jacobi approximation are dissussed. Then several orthogonal approximations in non-uniformly Jacobi weighted Sobolev spaces, and also Jacobi-Gauss-type interpolations are studied. These results are useful tools in the numerical solutions of differential and integral equations.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 2085984
zbMATH Keywords: Jacobi approximations
zbMATH Keywords: orthogonal projections
zbMATH Keywords: interpolations
reviewed by: Margit Lenard
MaRDI profile type: Publication
full work available at URL: j.jat.2004.03.008
OpenAlex ID: W2133964250
cites work: Q4052393
cites work: Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions
cites work: Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces
cites work: Q4112938
cites work: Q4256617
cites work: Techniques of scientific computing (Part 2)
cites work: Q4039908
cites work: Approximation Results for Orthogonal Polynomials in Sobolev Spaces
cites work: Spectral methods on triangles and other domains
cites work: A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations
cites work: Q4199478
cites work: On the Gibbs Phenomenon IV: Recovering Exponential Accuracy in a Subinterval from a Gegenbauer Partial Sum of a Piecewise Analytic Function
cites work: Spectral Methods and Their Applications
cites work: Gegenbauer approximation and its applications to differential equations on the whole line
cites work: Q4951037
cites work: Gegenbauer Approximation in Certain Hilbert Spaces and Its Applications to Singular Differential Equations
cites work: Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
cites work: A rational approximation and its applications to differential equations on the half line
cites work: Chebyshev rational spectral and pseudospectral methods on a semi‐infinite interval
cites work: Jacobi interpolation approximations and their applications to singular differential equations
cites work: Error analysis of spectral method on a triangle
cites work: Q3694635
cites work: Q4490850
cites work: Q3683006
cites work: Q3810338
cites work: On the Convergence of the p-Version of the Boundary Element Galerkin Method
cites work: Q5727762
DOI: 10.1016/J.JAT.2004.03.008
description: scientific article; zbMATH DE number 2085984