InterpolationLet . For given samples , the index set , of frequencies, we construct a -variate trigonometric polynomial
such that . Turning this into matrix vector notation, we aim to solve the system of linear equations
for the unknown vector of Fourier coefficients . We denote the vector of the given sample values by and the nonequispaced Fourier matrix by
We focus on the under-determined and consistent linear system , i.e., we expect to interpolate the given data , , exactly.
In particular, we incorporate damping factors , , and consider the optimal interpolation problem
This library of C functions computes approximations of (2) with the CGNE method.
The algorithms are implemented by Stefan Kunis in ./solver. Related paper are
Kunis, S. and Potts, D.
Stability Results for Scattered Data Interpolation by Trigonometric Polynomials.
SIAM J. Sci. Comput. 29, 1403 - 1419, (full paper ps, pdf) 2007