The Gibbs Phenomenon For A Class Of Interpolation Approximation

Because Gibbs phenomenon exists in many scientific problems, it attracts many researchers for long time. This article deals with Gibbs phenomenon for a kind of interpolation approximation. First of all, a convergence property is investigated; Secondly, a sufficient condition for Gibbs phenomenon is provided; Finally, an example is given.The thesis is organized as follows: in the first chapter, some related notations, definitions, the background and the main results are given; The Gibbs phenomenon for one dimensional interpolation approximation is studied in chapter 2; The last chapter extends its results of chapter 2 into two dimensional interpolation approximation for some special dilation matrix.