Stability Results for Scattered Data Interpolation by Trigonometric Polynomials

2007/02/01 by Stefan Kunis, Daniel Potts, Kunis, Stefan +1 · 1 citation
Earth and Planetary Sciences · Engineering · #65F10 #65F15 #65T40 #FOS: Mathematics #Geophysical Methods and Applications #Numerical Analysis (math.NA) #Numerical methods in engineering #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.math/0702019

openalex publication_date 2007/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems

Related

• Constructing spatial discretizations for sparse multivariate trigonometric polynomials that allow for a fast discrete Fourier transform
• A construction of linear bounded interpolatory operators on the torus
• Fast multi-dimensional scattered data approximation with Neumann boundary conditions
• Approximate Approximations from scattered data
• On Trigonometric Interpolation and Its Applications