An Adaptive Greedy Algorithm for Solving Large RBF Collocation Problems

被引：0
作者：
Y.C. Hon
R. Schaback
X. Zhou
机构：
[1] City University of Hong Kong,Department of Mathematics
[2] Kowloon Tong,Institute of Numerical and Applied Mathematics
[3] University of Göttingen,undefined
来源：
Numerical Algorithms | 2003年 / 32卷
关键词：
radial basis functions; adaptive; greedy; collocation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The solution of operator equations with radial basis functions by collocation in scattered points leads to large linear systems which often are nonsparse and ill-conditioned. But one can try to use only a subset of the data for the actual collocation, leaving the rest of the data points for error checking. This amounts to finding “sparse” approximate solutions of general linear systems arising from collocation. This contribution proposes an adaptive greedy method with proven (but slow) linear convergence to the full solution of the collocation equations. The collocation matrix need not be stored, and the progress of the method can be controlled by a variety of parameters. Some numerical examples are given.
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页码：13 / 25
页数：12
相关论文
共 22 条
[1]  
DeVore R.A.(1996)Some remarks on greedy algorithms Adv. Comput.Math. 5 173-187
[2]  
Temlyakov V.N.(1998)Convergence order estimates of meshless collocation methods using radial basis functions Adv. Comput. Math. 8 381-399
[3]  
Franke C.(1998)Solving partial differential equations by collocation using radial basis functions Appl. Math. Comput. 93 73-82
[4]  
Schaback R.(1999)Multiquadric collocation method with adaptive technique for problems with boundary layer Internat. J. Appl. Sci. Comput. 6 173-184
[5]  
Franke C.(1999)A multiquadric solution for the shallow water equations ASCE J. Hydraulic Engrg. 125 524-533
[6]  
Schaback R.(1998)An efficient numerical scheme for Burgers' equations Appl. Math. Comput. 95 37-50
[7]  
Hon Y.C.(2000)A quasi-interpolation method for solving stiff ordinary differential equations Internat. J. Numer. Methods Engrg. 48 1187-1197
[8]  
Hon Y.C.(1990)Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to hyperbolic, parabolic, and elliptic partial differential equations Comput. Math. Appl. 19 147-161
[9]  
Cheung K.F.(1994)An adaptive radial basis function approach to modeling scattered data J. Appl. Sci. Comput. 1 319-349
[10]  
Mao X.Z.(2000)Adaptive greedy techniques for approximate solution of large RBF systems Numer. Algorithms 24 239-254
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