正交复数B样条插值新方法  

A New Interpolation Method by Orthogonal Complex B-Spline

作　　者：郑力新[1] 周凯汀[1] 林福泳[2] 

机构地区：[1]华侨大学信息科学与工程学院 [2]华侨大学机电及自动化学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2009年第4期394-398,共5页Journal of Huaqiao University(Natural Science)

基　　金：教育部科学技术研究重点项目(207145);国务院侨办科研基金资助项目(07QZR02);福建省自然科学基金资助项目(A0610019);福建省高等学校新世纪优秀人才支持计划项目(07FJRC01)

摘　　要：研究利用复函数组{kξ(x)=eikx}的正交性,构造插值区域新的正交插值基函数,即正交复数B样条插值基函数,并给出任意阶正交复数B样条插值系数的通用计算公式.通过构造新的正交基,解除插值基及插值系数之间的耦合,将样条插值问题从求解N×N矩阵简化为使用一个显式公式直接同时求解,实现插值系数的并行计算.By using the orthogonal property of the complex function group {ξk（x）=e^ikx}, new orthogonal basis functions, i.e. orthogonal complex B-spline basis functions in the interpolation region are successively constructed. A general formula to compute coefficients of the orthogonal complex B-spline interpolation basis functions of arbitrary order is given. By constructing new orthogonal basis functions, the new method removes coupling of both the existing interpolation basis functions and the interpolation coefficients, and simplifies the interpolation task from solving a NX N matrix to simultaneously using one explicit computation formula directly. This realizes parallel computation of the interpolation coefficients.

关 键 词：插值 样条函数 正交函数 复值函数 并行计算 

分 类 号：TB115[理学—数学] O241.3[理学—应用数学]