Approximation properties of the $q$-sine bases
Spectral Theory
2015-05-19 v2 Numerical Analysis
Abstract
For the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional -Laplacian are known to form a Riesz basis of . We examine in this paper the approximation properties of this family of functions and its dual, in order to establish non-orthogonal spectral methods for the -Poisson boundary value problem and its corresponding parabolic time evolution initial value problem. The principal objective of our analysis is the determination of optimal values of for which the best approximation is achieved for a given problem.
Keywords
Cite
@article{arxiv.1008.2519,
title = {Approximation properties of the $q$-sine bases},
author = {Lyonell Boulton and Gabriel Lord},
journal= {arXiv preprint arXiv:1008.2519},
year = {2015}
}
Comments
20 pages, 11 figures and 2 tables. We have fixed a number of typos and added references. Changed the title to better reflect the content