S_2~1（△_（mn）^（2））插值样条函数的渐近展开

THE ASYMPTOTIC EXPANSIONS FOR S_2￣1(△_(mn)￣(2))INIERPOLATION SPLINE FUNCTION

利用二元样条空间Ｓ_２~１（△_（ｍｎ）^（２））的Ｂ样条基，本文讨论了带适当边界条件的中心插值问题，首次获得了非来积型二元样条插值的误差渐近展开．进一步，在边界条件（Ｂ）下，得到了十分简洁的渐近展式和在特殊点上的超收敛结果．

Using the B-spline basis of Bidimensional spline spaceS_2￣1(△_(mn)(2)).We discuss the centre interpolation spline function with appropriate boundary conditions. For the first time.We obtain the Asymptotic expansion of non-tensor product interpolating splines. Further more,we get the brief succinct Asymptotic expansion and super-convergence results at spe cial points (error bounds O(vh4))under the boundany condition (B).