【摘要】 本文讨论了一类凸四边形上的插值问题.指出这类插值问题是可解的,其解是分片二元三次多项式,且在凸四边形上是C~2-连续的.我们证明了这类插值问题的解的存在性和唯一性,给出了解样条的分片表达式及其逼近度的估计.最后还给出了一个应用实例和图形显示来说明本方法是可行的.更多还原

【Abstract】 In this paper we consider interpolation problems by bivariate cubic splines on quadrilaterals with C~2-continuous.An interpolation scheme is presented.The existence and uniqueness of the interpolation are given,and we also give the piecewise polynomial expression of the interpolating splines.The approximation order is discussed,and a numerical solution of PDE and graphical display are also provided.更多还原