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Efficient nonparametric density estimation on the sphere with applications in fluid mechanics

DSpace at IIT Bombay

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Title Efficient nonparametric density estimation on the sphere with applications in fluid mechanics
 
Creator EGECIOGLU, O
SRINIVASAN, A
 
Subject smoothed particle hydrodynamics
probability density
nonparametric estimation
fluid mechanics
convergence
kernel method
efficient algorithm
 
Description The application of nonparametric probability density function estimation for the purpose of data analysis is well established. More recently, such methods have been applied to fluid flow calculations since the density of the fluid plays a crucial role in determining the ow. Furthermore, when the calculations involve directional or axial data, the domain of interest falls on the surface of the sphere. Accurate and fast estimation of probability density functions is crucial for these calculations since the density estimation is performed at each iteration during the computation. In particular the values fn(X-1), f(n)(X-2),..., f(n)(X-n) of the density estimate at the sampled points X-i are needed to evolve the system. Usual nonparametric estimators make use of kernel functions to construct f(n). We propose a special sequence of weight functions for nonparametric density estimation that is especially suitable for such applications. The resulting method has a computational advantage over kernel methods in certain situations and also parallelizes easily. Conditions for convergence turn out to be similar to those required for kernel-based methods. We also discuss experiments on different distributions and compare the computational efficiency of our method with kernel based estimators.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T04:55:26Z
2011-12-26T12:58:25Z
2011-12-27T05:48:17Z
2011-08-29T04:55:26Z
2011-12-26T12:58:25Z
2011-12-27T05:48:17Z
2000
 
Type Article
 
Identifier SIAM JOURNAL ON SCIENTIFIC COMPUTING, 22(1), 152-176
1064-8275
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11965
http://hdl.handle.net/10054/11965
 
Language en