| 凸四边形上一类具有C~2-连续的插值问题的样条解及其应用 |
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| 引用本文： | 周天祥. 凸四边形上一类具有C~2-连续的插值问题的样条解及其应用[J]. 应用数学学报, 2009, 32(5) |
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| 作者姓名： | 周天祥 |
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| 作者单位： | 绍兴文理学院计算机系,绍兴,312000 |
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| 基金项目： | 浙江省重点学科(B类)计算数学基金和浙江省自然科学基金 |
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| 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.
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| 关 键 词： | 凸四边形 插值 二元三次样条 C~2.连续 逼近度 图形显示 |
On Interpolation and Approximation by Bivariate Cubic Splines with C~2-continuous on Convex Quadrilaterals |
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| ZHOU TIANXIANG. On Interpolation and Approximation by Bivariate Cubic Splines with C~2-continuous on Convex Quadrilaterals[J]. Acta Mathematicae Applicatae Sinica, 2009, 32(5) |
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| Authors: | ZHOU TIANXIANG |
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| Abstract: | In this paper we consider interpolation problems by bivariate cubic splines on quadrilaterals with C~2-continuons. An interpolation scheme is presented. The existence and uniqueness of the interpolation are given, and we also give the piecewise polynomial expres-sion of the interpolating splines. The approximation order is discussed, and a numerical solution of PDE and graphical display are also provided. |
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| Keywords: | convex quadrilateral cell interpolation bivariate cubic spline C~2-continuous approximation order graphical display |
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