昆明理工大学学报（自然科学版）
昆明理工大學學報（自然科學版）
곤명리공대학학보（자연과학판）
JOURNAL OF KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY（SCIENCE AND TECHNOLOGY）
2014年
4期
143-148
,共6页
矩阵切触有理插值%有理基函数%插值算子%插值函数
矩陣切觸有理插值%有理基函數%插值算子%插值函數
구진절촉유리삽치%유리기함수%삽치산자%삽치함수
matrix-valued osculatory rational interpolation%rational primary function%interpolation operator%interpolation function
矩阵切触有理插值的传统方法是连分式。连分式的优点是：格式相对固定，迭代方便；缺点是：算法的可行性是有条件的，且计算繁琐，可能出现极点或不可达点等。为了克服上述缺陷，提出了一种有别于连分式的矩阵切触有理插值的新方法。首先构造基函数及Tailor型插值算子，然后将二者作线性组合，得出各阶导数条件下的矩阵切触有理插值函数公式，证明了相应的定理，给出了误差估计及插值函数的一般计算步骤。本文的方法简单，计算量小，不需要任何附加条件，所构造的Tailor型插值算子具有承袭性，所得插值函数无极点和不可达点。数值例子说明了该方法的有效性和实用性。
矩陣切觸有理插值的傳統方法是連分式。連分式的優點是：格式相對固定，迭代方便；缺點是：算法的可行性是有條件的，且計算繁瑣，可能齣現極點或不可達點等。為瞭剋服上述缺陷，提齣瞭一種有彆于連分式的矩陣切觸有理插值的新方法。首先構造基函數及Tailor型插值算子，然後將二者作線性組閤，得齣各階導數條件下的矩陣切觸有理插值函數公式，證明瞭相應的定理，給齣瞭誤差估計及插值函數的一般計算步驟。本文的方法簡單，計算量小，不需要任何附加條件，所構造的Tailor型插值算子具有承襲性，所得插值函數無極點和不可達點。數值例子說明瞭該方法的有效性和實用性。
구진절촉유리삽치적전통방법시련분식。련분식적우점시：격식상대고정，질대방편；결점시：산법적가행성시유조건적，차계산번쇄，가능출현겁점혹불가체점등。위료극복상술결함，제출료일충유별우련분식적구진절촉유리삽치적신방법。수선구조기함수급Tailor형삽치산자，연후장이자작선성조합，득출각계도수조건하적구진절촉유리삽치함수공식，증명료상응적정리，급출료오차고계급삽치함수적일반계산보취。본문적방법간단，계산량소，불수요임하부가조건，소구조적Tailor형삽치산자구유승습성，소득삽치함수무겁점화불가체점。수치례자설명료해방법적유효성화실용성。
The traditional method of matrix-valued osculatory rational interpolation is continued fraction,which enjoys some advantages.The former include relatively constant format and convenient iteration.The latter include conditional feasibility,complicated calculation and possibility of poles or inaccessible points.In order to overcome the disadvantages,another method of matrix-valued osculatory rational interpolation which is different from continued fraction is proposed in this paper.The primary function and the Tailor type interpolation operators are firstly constructed,which are then combined linearly to work out the formulas of matrix-valued osculatory rational interpolating function under the conditions of all order derivatives.Corresponding theorems are then proved.The error estimation and general steps of calculating interpolation functions are finally given.This method is simple with little calculation and no additional conditions.The constructed Tailor type interpolation operators are inherited.The interpolating function can be easily worked out with no poles and inaccessible points.The efficiency and practicability of the proposed method is illustrated by a numerical example.
