合肥师范学院学报
閤肥師範學院學報
합비사범학원학보
JOURNAL OF ANHUI INSTITUTE OF EDUCATION
2012年
3期
1-4,10
,共5页
连分式%有理插值%特征定理%误差分析
連分式%有理插值%特徵定理%誤差分析
련분식%유리삽치%특정정리%오차분석
continued fractioN%rational interpolatioN%characteristic theorem%error analysis
文章基于Stieltijes型分叉连分式有理插值，结合Thiele型连分式及Newton多项式，构造了一种方形网格上的二元混合有理插值函数，通过定义偏差商、偏逆差商和混合逆差商建立递推算法。构造的这种有理插值函数满足有理插值P1题中所给的插值条件，并给出了插值的特征定理及其证明，进行了误差分析，最后给出的数值例子，验证了所给算法的有效性。
文章基于Stieltijes型分扠連分式有理插值，結閤Thiele型連分式及Newton多項式，構造瞭一種方形網格上的二元混閤有理插值函數，通過定義偏差商、偏逆差商和混閤逆差商建立遞推算法。構造的這種有理插值函數滿足有理插值P1題中所給的插值條件，併給齣瞭插值的特徵定理及其證明，進行瞭誤差分析，最後給齣的數值例子，驗證瞭所給算法的有效性。
문장기우Stieltijes형분차련분식유리삽치，결합Thiele형련분식급Newton다항식，구조료일충방형망격상적이원혼합유리삽치함수，통과정의편차상、편역차상화혼합역차상건립체추산법。구조적저충유리삽치함수만족유리삽치P1제중소급적삽치조건，병급출료삽치적특정정리급기증명，진행료오차분석，최후급출적수치례자，험증료소급산법적유효성。
In this paper, bivariate blending rational interpolation function was constructed based on stieltijes＇ branched continued fraction, Thiele rational interpolation and Newton polynomial. By defining the partial difference, the partial inverse difference and blending inverse difference building the recursive algorithm. The bivariate rational function which interpolates the given support points, and interpolating characteristic theorem and its proof is given, also error analysis.. Numerical examples are given to show the effectiveness of the result.
