CAJ | 학술논문

提出了一类定义在矩形网格上的二阶多元混合切触有理插值格式,记作SNm,n(x,y).新的插值格式由Salzer型插值连分式和扩展的Newton插值多项式综合构造而成.数值例子显示相对于多项式插值格式,利用混合切触有理插值格式SNm,n(x,y)可以得到较小的逼近误差,特别地,对于存在渐近线的被插函数,实例表明新方法比传统的多项式方法具有更好的逼近效果.
제출료일류정의재구형망격상적이계다원혼합절촉유리삽치격식,기작SNm,n(x,y).신적삽치격식유Salzer형삽치련분식화확전적Newton삽치다항식종합구조이성.수치례자현시상대우다항식삽치격식,이용혼합절촉유리삽치격식SNm,n(x,y)가이득도교소적핍근오차,특별지,대우존재점근선적피삽함수,실례표명신방법비전통적다항식방법구유경호적핍근효과.
A scheme for multivariate blending osculatory rational interpolation of order two has been constructed based on rectangular grids. The new interpolation function is denoted by SNm,n(x,y) and can be constructed by incorporating both Salzer's interpolating continued fractions and the expansive Newton's interpolating polynomials. Furthermore, numerical examples are illustrated to show the approximation effects using the multivariate osculatory rational interpolation method by the constructed function SNm,n(x,y) in the end. Especially, in the case of sharp curves, illustration shows that the presented method demonstrates a better approximation effect, whereas it is sometimes inoperative using polynomial interpolation methods.