成果/Result
- SMOOTHNESS EQUIVALENCE PROPERTIES OF GENERAL MANIFOLD-VALUED DATA SUBDIVISION SCHEMES被引量：23收藏
- 作者：Xie, Gang Yu, Thomas P. -Y.
- 机构：E China Univ Sci & Technol;Drexel Univ
- 来源：MULTISCALE MODELING & SIMULATION 2008
- 关键词：subdivision manifold smoothness
- On a new proximity condition for manifold-valued subdivision schemes被引量：21收藏
- 作者：Duchamp, Tom Xie, Gang Yu, Thomas
- 机构： Department of Mathematics; Department of Mathematics; Department of Mathematics
- 来源：Springer Proceedings in Mathematics and Statistics 2014
- 关键词：Equivalence classes - Dynamical systems - Three dimensional computer graphics - Approximation algorithms
- Convergence of Online Gradient Method with Momentum for BP Neural Network被引量：21收藏
- 作者：Pan, Chengyan Xie, Gang
- 机构： School of Science
- 来源：IOP Conference Series: Earth and Environmental Science 2021
- 关键词：Backpropagation - Multilayer neural networks - Momentum - Network layers
- Smoothness equivalence properties of interpolatory Lie group subdivision schemes被引量：12收藏
- 作者：Xie, Gang Yu, Thomas P. -Y.
- 机构：Drexel Univ;E China Univ Sci & Technol
- 来源：IMA JOURNAL OF NUMERICAL ANALYSIS 2010
- 关键词：subdivision schemes Lie groups matrix Lie groups interpolation smoothness equivalence breakdown of smoothness equivalence
- Single Basepoint Subdivision Schemes for Manifold-valued Data: Time-Symmetry Without Space-Symmetry被引量：7收藏
- 作者：Duchamp, Tom Xie, Gang Yu, Thomas
- 机构：Univ Washington;E China Univ Sci & Technol;Drexel Univ
- 来源：FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2013
- 关键词：Nonlinear subdivision Affine connection Retraction Exponential map Riemannian manifold Symmetric space Curvature Time-symmetry
- Approximation order equivalence properties of manifold-valued data subdivision schemes被引量：6收藏
- 作者：Xie, Gang Yu, Thomas P-Y.
- 机构：E China Univ Sci & Technol;Drexel Univ
- 来源：IMA JOURNAL OF NUMERICAL ANALYSIS 2012
- 关键词：approximation order subdivision scheme nonlinear subdivision scheme interpolation quasiinterpolation manifold
- Smoothing nonlinear subdivision schemes by averaging被引量：6收藏
- 作者：Duchamp, Tom Xie, Gang Yu, Thomas
- 机构：Univ Washington;East China Univ Sci & Technol;Drexel Univ
- 来源：NUMERICAL ALGORITHMS 2018
- 关键词：Averaging Differential proximity condition Nonlinear subdivision B-Spline Lane-Riesenfeld algorithm Manifold
- A Necessary and Sufficient Proximity Condition for Smoothness Equivalence of Nonlinear Subdivision Schemes被引量：3收藏
- 作者：Duchamp, Tom Xie, Gang Yu, Thomas
- 机构：Univ Washington;East China Univ Sci & Technol;Drexel Univ
- 来源：FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2016
- 关键词：Differential proximity condition Nonlinear subdivision Manifold Curvature Symmetry Super-convergence Zgymund class Dynamical system Poincare-Dulac normal form Resonance
- 带动量项的梯度下降算法的收敛性被引量：3收藏
- 作者：彭先伦 谢纲
- 机构：华东理工大学数学学院
- 来源：《华东理工大学学报（自然科学版）》 2021
- 关键词：神经网络 反向传播算法 动量 动量系数 收敛
- 摘要：本文对基于三层前馈神经网络的带动量项的反向传播算法进行了理论分析。在我们的模型中,学习率为常数,动量系数为一个适应性的变量。本文给出了带动量项的反向传播算法的收敛性结果及详细的证明。相比于目前已有的结果,本文中的结论更具...
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- 四点插值细分算法的光滑度被引量：3收藏
- 作者：索园园 欧颖豪 谢纲
- 机构：华东理工大学数学系
- 来源：《科学技术与工程》 2011
- 关键词：细分 插值 光滑度 特征值 广义特征向量
- 摘要：将Dyn,Levin,和Gregory关于四点插值细分算法极限曲线的光滑性的结论从细分权值对称的情形推广到权值不对称的情形,并给出了此情形下四点插值细分算法极限曲线具有连续的一阶导数的充分条件和必要条件。同时还利用矩阵的...
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- Invariance property of proximity conditions in nonlinear subdivision被引量：2收藏
- 作者：Xie, Gang Yu, Thomas P. Y.
- 机构：E China Univ Sci & Technol;Drexel Univ
- 来源：JOURNAL OF APPROXIMATION THEORY 2012
- 关键词：Nonlinear subdivision Proximity condition Manifold Coordinate independence Hermite-Biehler theorem
- Study a new mesh simplification method in reverse engineering被引量：0收藏
- 作者：Zhao, Hongqing Yang, Yanzhen Xie, Gang
- 机构：East China Univ Sci & Technol;Shangdong Jiaotong Univ
- 来源：SECOND INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL INTELLIGENCE AND DESIGN, VOL 2, PROCEEDINGS 2009
- 关键词：mesh simplification changing rate of surface subdivision surface reverse engineering
