基于双二次B样条的拟插值算子的构造

Construction of Quasi-interpolation Operators by Biquadratic B-spline

对数据点{(xi,yj),f(xi,yj)},(i=0,1,…,n;j=0,1,…,m),应用双二次B样条基函数构造了一种双变量拟插值算子(Lf)(x,y),证明了算子(Lf)(x,y)具有二次多项式再生性,并给出了其逼近误差,最后通过数值模拟说明了该算子的可行性.

Using biquadratic B-spline basis function,we have constructed a bivariate quasi-interpolation operator （Lf）（x,y） for data points {（xi,yj）, f（xi,yj）},（i=0,1,…,n; j= 0,1,…,m）. The quasi-interpolation operator （ Lf ） （ x, y ） can reproduce quadratic polynomial, and approximation error of the quasi-interpolation operator is given. Finally,we give some numerical experiments to illustrate the feasibility of the operator.