Local approximation on surfaces with discontinuities, given limited order Fourier coefficients (Q932742)

The author presents a local spline approximation of a bivariate function \(f\) with jump discontinuities along curves. Assume that \(f\) is smooth except for these jump discontinuities and that \(f\) is given by a limited number of its (noisy) Fourier coefficients. Then spline approximations of 1-D sections of \(f\) are constructed by a method of the author [J. Comput. Appl. Math. 164--165, 783--795 (2004; Zbl 1039.41006)]. By blending a finite number of these 1-D approximations, a local approximation scheme of \(f\) is obtained.