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RESEARCH PAPERS

A Statistical Study of Generalized Cell Mapping

[+] Author and Article Information
Jian-Qiao Sun, C. S. Hsu

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Appl. Mech 55(3), 694-701 (Sep 01, 1988) (8 pages) doi:10.1115/1.3125851 History: Received April 24, 1987; Revised March 29, 1988; Online July 21, 2009

Abstract

In this paper a statistical error analysis of the generalized cell mapping method for both deterministic and stochastic dynamical systems is examined, based upon the statistical analogy of the generalized cell mapping method to the density estimation. The convergence of the mean square error of the one step transition probability matrix of generalized cell mapping for deterministic and stochastic systems is studied. For stochastic systems, a well-known trade-off feature of the density estimation exists in the mean square error of the one step transition probability matrix, which leads to an optimal design of generalized cell mapping for stochastic systems. The conclusions of the study are illustrated with some examples.

Copyright © 1988 by ASME
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