Stability Results for Scattered Data Interpolation by Trigonometric Polynomials
数值分析
2007-05-23 v1
摘要
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the fast Fourier transforms for nonequispaced nodes. The main result is that under mild assumptions the total complexity for solving the interpolation problem at M arbitrary nodes is of order O(M logM). This result is obtained by the use of localised trigonometric kernels where the localisation is chosen in accordance to the spatial dimension d. Numerical examples show the efficiency of the new algorithm.
引用
@article{arxiv.math/0702019,
title = {Stability Results for Scattered Data Interpolation by Trigonometric Polynomials},
author = {Stefan Kunis and Daniel Potts},
journal= {arXiv preprint arXiv:math/0702019},
year = {2007}
}
备注
21 pages, 5 figures