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许跃生 《应用数学和力学(英文版)》1984,(3)
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given. 相似文献
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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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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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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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许跃生 《应用数学和力学(英文版)》1985,(3)
In this paper,we give recurrence formula for normalized B-Splines with respect tostandard system{(?)~(i-1)(x)}_(i-1)~m which is the basic set of solutions to a class of differentialoperators in view of generalized divided difference—Green function—B-Splines. 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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