一种基于截断多项式的三角域V-系统构造  

A kind of atriangular V-system construction scheme based on truncated polynomial function

作　　者：王相海[1,2] 刘乙萱 曲思洁 李炜 宋传鸣[1] WANG Xianghai;LIU Yixuan;QU Sijie;LI Wei;SONG Chuanming(School of Computer and Information Technology, Liaoning Normal University, Dalian 116029, China;School of Mathematics, Liaoning Normal University, Dalian 116029, China)

机构地区：[1]辽宁师范大学计算机与信息技术学院,辽宁大连116029 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2021年第3期335-341,共7页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(41671439);辽宁省高等学校教育厅创新团队支持计划项目(LT2017013)。

摘　　要：U-系统和V-系统的出现和发展为连续和非连续信号的有效表达提供了一种新的思路.在对V-系统和三角域自相似剖分分析的基础上,提出了一种基于截断多项式的三角域V-系统构造方法.给出了三角域上的k次V-系统生成元和截断多项式的定义.依据三角域的自相似剖分结构从截断多项式和分片的Legendre多项式出发,构造了一种三角域上的V-系统生成元,并以三角域上的1次V-系统为例对所构造V-系统的表现形式给出了数学解析表达式.对所构造V-系统的性质进行了分析和证明.The emergence and development of U-and V-systems provide a new idea for effective expression of renewal signals and discrete signals.One-time V-system construction method is proposed based on orthogonal triangle domain iterative segmentation.Firstly,a non-uniform iterative method for segmentation on a right-angled triangle is proposed.The self-similarity of the triangle can be as a special case,a set of linearly independent function groups is selected on the triangular domain under the level 1 iterative splitting,and the function group is orthogonally unitized to obtain mutually orthogonal generators;further by performing generator elements rotation,compression,translation and other operations generate other functions of the V-system.Finally,the characteristics of the constructed V-system are studied.This scheme provides a new idea for the construction of the V-system on the triangular domain.

关 键 词：V-系统 三角域 截断多项式函数 生成元 非连续正交系 剖分 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]