合肥学院学报：自然科学版
閤肥學院學報：自然科學版
합비학원학보：자연과학판
Journal of Hefei University :Natural Sciences
2012年
4期
26-30
,共5页
连分式%Lagrange多项式%有理插值%特征定理
連分式%Lagrange多項式%有理插值%特徵定理
련분식%Lagrange다항식%유리삽치%특정정리
continued fractions%Lagrange polynomial%rational interpolation%characterization theorems
Thiele型连分式在有理插值问题中有着重要的应用，它通过定义反差商构造给定结点上的有理函数，其表达式简单、计算方便．现将一元Thiele型连分式与一元Lagrange插值基函数结合起来，构造矩形网格上的Lagrange-Thiele型二元有理插值函数，通过定义偏逆差商，建立递推算法，构造的Lagrange--Thiele型有理插值函数满足有理插值问题中所给的插值条件，并给出了插值的特征定理及对偶性，最后给出数值例子，验证了所给算法的有效性．
Thiele型連分式在有理插值問題中有著重要的應用，它通過定義反差商構造給定結點上的有理函數，其錶達式簡單、計算方便．現將一元Thiele型連分式與一元Lagrange插值基函數結閤起來，構造矩形網格上的Lagrange-Thiele型二元有理插值函數，通過定義偏逆差商，建立遞推算法，構造的Lagrange--Thiele型有理插值函數滿足有理插值問題中所給的插值條件，併給齣瞭插值的特徵定理及對偶性，最後給齣數值例子，驗證瞭所給算法的有效性．
Thiele형련분식재유리삽치문제중유착중요적응용，타통과정의반차상구조급정결점상적유리함수，기표체식간단、계산방편．현장일원Thiele형련분식여일원Lagrange삽치기함수결합기래，구조구형망격상적Lagrange-Thiele형이원유리삽치함수，통과정의편역차상，건립체추산법，구조적Lagrange--Thiele형유리삽치함수만족유리삽치문제중소급적삽치조건，병급출료삽치적특정정리급대우성，최후급출수치례자，험증료소급산법적유효성．
Thiele' continued fractions have the important application in rational interpolation , which is constructed on the given interpolating points by defining inverse differedces, it is calculated handly and has simple expression. In this paper, Lagrange-Thiele type bivariate rational interpolation has been constructed over rectangular grid based on one dimensional Thiele-continued fractions and combined with the basic function of Lagrange interpolation, by defining partial inverse differences, the recursive algorithm is given . The Lagrange-Thiele rational interpolating function is satisfied with the given interpolating conditions, the characterization theorems of the rational function and duality are carried out. At last, we present a example of this kind of interpolation to illustrate the effectiveness of the interpolating algorithms.
