Geodesic
Analytical description for application of 1D Kohonen scheme for constructing adaptive meshes
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 2, pp. 131-140

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In this paper, the analysis of analytical approaches to investigation of an asymptotical disposition for a special iterative discrete-stochastic algorithm for constructing adaptive meshes using the Kohonen self-organizing maps is made. For a simplified one-dimensional case, a “recurrent” approach to obtaining mean most probable dispositions of grid nodes for a small number of iterations has been developed. This approach allows one to conduct interesting analytical investigations and numerical testing for the algorithm considered. 
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     author = {A. V. Voytishek and D. S. Khmel},
     title = {Analytical description for application of {1D} {Kohonen} scheme for constructing adaptive meshes},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_2_a1/}
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A. V. Voytishek; D. S. Khmel. Analytical description for application of 1D Kohonen scheme for constructing adaptive meshes. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 2, pp. 131-140. http://geodesic.mathdoc.fr/item/SJVM_2011_14_2_a1/