Asymptotic Independence and Uniform Distribution of Quantization Errors for Spatially Discretized Dynamical Systems
1998 ◽
Vol 08
(07)
◽
pp. 1479-1490
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Keyword(s):
Computer simulation of dynamical systems involves a state space which is the finite set of computer arithmetic. Restricting state values to this grid produces roundoff effects which can be studied by replacing the original system with a spatially discretized dynamical system. Study of the deviation of the discretized trajectories from those of the original system reduces to that of appropriately defined quantization errors. As the grid is refined, the asymptotic behavior of these quantization errors follows probabilistic laws. These results are applied to discretized polynomial mappings of the unit interval.
Keyword(s):
Keyword(s):
2011 ◽
Vol 369
(1939)
◽
pp. 1118-1136
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2007 ◽
Vol 5
◽
pp. 195-200
1989 ◽
Vol 03
(15)
◽
pp. 1185-1188
◽
2008 ◽
Vol 28
(5)
◽
pp. 1509-1531
◽