辽宁师范大学学报(自然科学版)
遼寧師範大學學報(自然科學版)
료녕사범대학학보(자연과학판)
JOURNAL OF LIAONING NORMAL UNIVERSITY(NATURAL SCIENCE)
2015年
2期
145-149
,共5页
崔利宏%孟敏%李笑笑%高小淞
崔利宏%孟敏%李笑笑%高小淞
최리굉%맹민%리소소%고소송
多元Lagrange插值%二次曲面插值%可解结点组
多元Lagrange插值%二次麯麵插值%可解結點組
다원Lagrange삽치%이차곡면삽치%가해결점조
multivariate Lagrange interpolation%interpolation on quadratic surfaces%the set of nodes for solvable
以二元函数Lagrange插值研究结果为基础,对三元函数Lagrange插值结点组可解性问题进行了研究,提出了二次曲面充分相交和二次曲面上Lagrange插值可解结点组的基本概念,研究了二次曲面插值可解结点组的某些基本理论和拓扑结构,得到了构造二次代数曲面和二次空间代数曲线插值可解结点组的添加二次曲面法。这些方法都是以迭加方式构造完成的,这对于编译计算机算法程序,进而在计算机上自动完成插值可解结点组的构造,并得到插值格式创造了十分便利的条件。最后给出了实例验证算法的有效性。
以二元函數Lagrange插值研究結果為基礎,對三元函數Lagrange插值結點組可解性問題進行瞭研究,提齣瞭二次麯麵充分相交和二次麯麵上Lagrange插值可解結點組的基本概唸,研究瞭二次麯麵插值可解結點組的某些基本理論和拓撲結構,得到瞭構造二次代數麯麵和二次空間代數麯線插值可解結點組的添加二次麯麵法。這些方法都是以迭加方式構造完成的,這對于編譯計算機算法程序,進而在計算機上自動完成插值可解結點組的構造,併得到插值格式創造瞭十分便利的條件。最後給齣瞭實例驗證算法的有效性。
이이원함수Lagrange삽치연구결과위기출,대삼원함수Lagrange삽치결점조가해성문제진행료연구,제출료이차곡면충분상교화이차곡면상Lagrange삽치가해결점조적기본개념,연구료이차곡면삽치가해결점조적모사기본이론화탁복결구,득도료구조이차대수곡면화이차공간대수곡선삽치가해결점조적첨가이차곡면법。저사방법도시이질가방식구조완성적,저대우편역계산궤산법정서,진이재계산궤상자동완성삽치가해결점조적구조,병득도삽치격식창조료십분편리적조건。최후급출료실례험증산법적유효성。
Based on the results for bivariate function Lagrange interpolation ,the solvability problem for trivariate function interpolation are studied .The quadric surfaces complete intersection and the solvability of Lagrange interpolation nodes on the set of basic concept are proposed .The quadric in‐terpolation nodes set some of the basic theory and topology are investigated ,the structure of quadrat‐ic algebraic surface and the space algebra curve interpolation node set to add quadric surface method are obtained .T hese methods are based on the superposition method constructed w hich has created a very convenient conditions ,to compile the program of computer algorithm ,and then solve automati‐cally interpolation of the structure of the node set and get the interpolation format on the computer . A numerical example is given to verify the validity of the algorithm .