The Dangers of Rounding Errors for Simulations and Analysis of Nonlinear Circuits and Systems-and How to Avoid Them

被引：52
作者：
Galias, Zbigniew [1 ]
机构：
[1] AGH Univ Sci & Technol, Dept Elect Engn, PL-30059 Krakow, Poland
来源：
IEEE CIRCUITS AND SYSTEMS MAGAZINE | 2013年 / 13卷 / 03期
关键词：
TOPOLOGICAL-ENTROPY; CHUAS CIRCUIT; EQUATIONS; ORBITS; CHAOS; PROOF; SETS;
D O I：
10.1109/MCAS.2013.2271444
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
Due to rounding errors results obtained by numerical simulations of nonlinear systems may be unreliable. It is however possible to carry out the computations in such a way that the results obtained are rigorous. In this paper several tools based on interval analysis are presented. Methods for computing trajectories, techniques for finding accurate enclosures of attractors, interval operators for proving the existence of fixed points and periodic orbits, and methods for proving the existence of nontrivial symbolic dynamics, are described. Computational techniques are illustrated by performing validated numerical analysis of the Henon map and the Chua's circuit.
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收藏
页码：35 / 52
页数：18
相关论文
共 44 条
[1]  
Alefeld G., 1983, Introduction to Interval Computation
[2]  
[Anonymous], TOPOL METHODS NONLIN
[3]  
[Anonymous], STUDIES COMPUTATIONA
[4]   EXPLORING CHAOTIC MOTION THROUGH PERIODIC-ORBITS [J].
AUERBACH, D ;
CVITANOVIC, P ;
ECKMANN, JP ;
GUNARATNE, G ;
PROCACCIA, I .
PHYSICAL REVIEW LETTERS, 1987, 58 (23) :2387-2389
[5]  
Bendtsen C., 1996, Technical Report IMM-REP-1996-17
[6]  
Berz M., 1998, Reliable Computing, V4, P361, DOI 10.1023/A:1024467732637
[7]   CANONICAL REALIZATION OF CHUA CIRCUIT FAMILY [J].
CHUA, LO ;
LIN, GN .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1990, 37 (07) :885-902
[8]   INVARIANT MEASUREMENT OF STRANGE SETS IN TERMS OF CYCLES [J].
CVITANOVIC, P .
PHYSICAL REVIEW LETTERS, 1988, 61 (24) :2729-2732
[9]   Adaptive enumeration of implicit surfaces with affine arithmetic [J].
deFigueiredo, LH ;
Stolfi, J .
COMPUTER GRAPHICS FORUM, 1996, 15 (05) :287-296
[10]   Finding zeros by multilevel subdivision techniques [J].
Dellnitz, M ;
Schütze, O ;
Sertl, S .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2002, 22 (02) :167-185
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