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自适应稀疏伪谱逼近新方法

本站小编 Free考研考试/2021-12-27

林济铿1, 袁恺明1, 申丹枫1, 罗萍萍2, 刘阳升1
1. 同济大学电子与信息工程学院, 上海 201804;
2. 上海电力大学电气工程学院, 上海 200090
收稿日期:2018-06-22出版日期:2020-02-15发布日期:2020-02-15




A NEW ADAPTIVE SPARSE PSEUDOSPECTRAL APPROXIMATION METHOD

Lin Jikeng1, Yuan Kaiming1, Shen Danfeng1, Luo Pingping2, Liu Yangsheng1
1. College of Electronics and Information Engineering, Tongji University, Shanghai 201804, China;
2. College of Electrical Engineering, Shanghai Electrical Power University, Shanghai 200090, China
Received:2018-06-22Online:2020-02-15Published:2020-02-15







摘要



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自适应稀疏伪谱逼近法是广义混沌多项式类方法的最新进展,相对于其它方法具有计算精度高、速度快的优点.但它仍存在如下缺点:1)终止判据对逼近误差的估计精度偏低;2)只适用于单输出问题.本文提出了适用于多输出问题且具有更高逼近精度的自适应稀疏伪谱逼近新方法.本文首先提出了新型终止判据及基于此新型终止判据的自适应稀疏伪谱逼近新方法,并以命题的形式证明了新型终止判据相比于现有终止判据具有更高的估计精度,从而使基于此的逼近函数精度更接近于预期精度;进而,本文基于指标集的统一策略和新型终止判据,提出了适用于多输出问题的自适应稀疏伪谱逼近新方法,该方法因能充分利用各输出变量的抽样结果,具有比将单输出方法直接推广到多输出问题更高的计算效率.多个算例验证了本文所提出新方法的有效性和正确性.
MR(2010)主题分类:
65D15
65Y20

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