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MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS   总被引:5,自引:0,他引:5  
We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstra  相似文献
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陈仲英  巫斌  许跃生 《东北数学》2005,21(2):233-252
We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.  相似文献
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利用“构造性贪婪算法(CGS)”构造目标函数的小波树逼近. 首先定义了一个函数类, 对此函数类中的每个函数, 由CGS生成的分片多项式逼近都具有给定的收敛阶. 其次通过研究所定义函数类的嵌入性质讨论了该函数类和其他已知函数空间的关系. 在小波树逼近领域, 给出了使小波树逼近达到最优收敛阶的一个充分条件. 最后证明, 如果树结构是用CGS生成的, 则相应的小波树逼近具有最优收敛阶.  相似文献
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对边值问题(2)采用下述离散化方法:在x方向上用差分离散,得半离散的常微分方程组  相似文献
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本文从广义差商-Green函数-B样条的观点出发,绘出了以正则系统{(?)~(i-1)(x)}_(i-1)~m为基解组的一类微分算子的正规B样条的递推公式.  相似文献
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本文研究具有幂基解组的微分算子所定义的广义差商的Leibniz公式及其格林(Green)函数的递推关系。  相似文献
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前言          下载免费PDF全文
许跃生  陆遥 《计算数学》2017,39(4):337-338
<正>"广东省计算数学研究进展"是由《计算数学》主编周爱辉研究员委托中山大学许跃生教授和陆遥教授组稿编辑、以反映广东省计算数学和高性能计算领域最新研究进展的专辑。本专辑于2016年开始组稿,历时一年多,经过约稿、专家评审和定稿。今天终于看到"高维带宽有限随机信号从平均过采样的指数阶逼近"等八篇论文组成的"广东省计算数学研究进展"专辑即将付梓出版,该专辑展示了广东省计算数学最新进展的一个侧面。  相似文献
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