ON A NEW TYPE OF MIXED INTERPOLATION

被引：45

作者：

DEMEYER, H ^{[1
]}

VANTHOURNOUT, J ^{[1
]}

VANDENBERGHE, G ^{[1
]}

机构：

[1] STATE UNIV GHENT,NUMERIEKE WISKUNDE & INFORMAT LAB,B-9000 GHENT,BELGIUM

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1990年 / 30卷 / 01期

关键词：

error term; forward and backward differences; Interpolation function; mixed and polynomial interpolation;

D O I：

10.1016/0377-0427(90)90005-K

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We approximate every function f by a function fn(x) of the form a cos kx + b sin kx + Σn-2i=0cixi so that f(jh) = fn(jh) for the n + 1 equidistant points jh, j = 0,..., n. That interpolation function fn(x) is proved to be unique and can be written as the sum of the nth-degree interpolation polynomial based on the same points and two correction terms. The error term is also discussed. The results for this mixed type of interpolation reduce to the known results of the polynomial case as the parameter k is tending to 0. This new interpolation theory will be used in the future for the construction of quadrature rules and multistep methods for ordinary differential equations. © 1990.

引用

页码：55 / 69

页数：15

共 15 条

[1] NUMERICAL INTEGRATION OF PRODUCTS OF FOURIER AND ORDINARY POLYNOMIALS [J].