基于ternary细分的Gibbs现象分析  

Analysis of the Gibbs phenomenon in ternary subdivision schemes

作　　者：周洁 郑红婵[1] 贺兴时[2] ZHOU Jie;ZHENG Hongchan;HE Xingshi(School of Natural&Applied Sciences,Northwestern Polytechnical University,Xi’an 710129,China;School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西北工业大学理学院,陕西西安710129 [2]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2018年第4期503-510,共8页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(71401134;71571144);陕西省自然科学基础研究计划项目(2015JM6056)

摘　　要：将binary细分法推广到ternary细分法下,基于该细分法讨论Gibbs现象.系统地分析了ternary细分法Gibbs现象产生的原因.通过探讨ternary细分法mask值的部分和的正负性,提出一个充分条件来判断Gibbs现象的存在性以及规避方法.分别以3点ternary细分法和5点ternary细分法为例,利用数值实验证实结果的合理性.The results of binary subdivision schemes are generalized to ternary subdivision schemes,the Gibbs phenomenon is discussed based on this subdivision schemes.The cause of Gibbs phenomenon is analyzed systematically.By considering the masks of ternary subdivision schemes,a sufficient condition is obtained to determine whether there exists a Gibbs phenomenon for ternary subdivision schemes in the limit function close to the discontinuous point.By applying this condition,the Gibbs phenomenon is avoided for ternary subdivision schemes near discontinuity points.Some examples in classical subdivision schemes are given to verify the results.

关 键 词：ternary细分 Gibbs现象 小波展开 傅里叶级数 

分 类 号：O242.2[理学—计算数学]