Error Analysis for a Noisy Lacunary Cubic Spline Interpolation and a Simple Noisy Cubic Spline Quasi Interpolation

摘要

We mainly present the error analysis for two new cubic spline based methods; one is a lacunary interpolation method and the other is a very simplequasi interpolation method. The new methods are able to reconstruct a function and its first two derivatives from noisy function data. The explicit error bounds for the methodsare given and proved. Numerical tests and comparisons are performed. Numerical results verify the efficiency of our methods.