三种Multiquadric拟插值多项式的再生性

Property of Polynomial Reproducing for Three Kinds of Multiquadric Quasi-interpolation

先研究了三种已知的Multiquadric拟插值的再生性,然后对三种已知的Multiquadric拟插值进行了推广,进一步讨论推广后的拟插值多项式的再生性,得到了如下结果:L_A不是常数再生的;当a+b=1时,L_D是常数再生的,但非线性再生的;当a=1/2,b=1/2时,L_D是线性再生的,但非二次多项式再生的.

In this paper, we study the property of polynomial reproducing for three kinds of known MQ quasi-interpolation firstly, and deduce that LA isn＇t constant reproducing, LB is constant reproducing but not linear reproducing. Lo is linear reproducing but not quadratic polynomial reproducing. Next to modifying the three kinds of MQ quasi- interpolation, further discussion property reproducing of the modified quasi-interpolation polynomial, and deduce that LAisn＇t constant reproducing; LB is constant reproducing but not linear reproducing when a ＋ b = 1; LD is linear reproducing but not quadratic polynomial reproducing whena=1/2, b=1/2.