On Approximation of Smooth Functions by L-Splines at a Point

摘要

We constructed "almost interpolation" generalized Z-splines based on the basis functions, composed of parts of solutions of the differential equation, which coefficients change from segment to segment. Estimate of error for approximation by these splines of smooth functions at arbitrary point were obtained and we proved superconvergence in nodes of spline, which approximates functions holding the same differential equation as the built splines.