Finding positively invariant sets of a class of nonlinear loops via curve fitting

Liyong Shen; Min Wu; Zhengfeng Yang; Zhenbing Zeng

doi:10.1145/1577190.1577218

Finding positively invariant sets of a class of nonlinear loops via curve fitting

Liyong Shen^*
, Min Wu
, Zhengfeng Yang
, Zhenbing Zeng

^*Corresponding author for this work

Software Engineering Institute

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In this paper, we study positively invariant sets of a class of nonlinear loops and discuss the relation between these sets and the attractors of the loops. For the canonical Hénon map, a numerical method based on curve fitting is proposed to find a positively invariant set containing the strange attractor. This work can be generalized to find inequality termination conditions for loops with nonlinear assignments

Original language	English
Title of host publication	Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009
Pages	185-190
Number of pages	6
DOIs	https://doi.org/10.1145/1577190.1577218
State	Published - 2009
Event	2009 Conference on Symbolic Numeric Computation, SNC 2009 - Kyoto, Japan Duration: 3 Aug 2009 → 5 Aug 2009

Publication series

Name	Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009

Conference

Conference	2009 Conference on Symbolic Numeric Computation, SNC 2009
Country/Territory	Japan
City	Kyoto
Period	3/08/09 → 5/08/09

Keywords

Curve fitting
Hénon map
Positively invariant sets
Program verification

Access to Document

10.1145/1577190.1577218

Cite this

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title = "Finding positively invariant sets of a class of nonlinear loops via curve fitting",

abstract = "In this paper, we study positively invariant sets of a class of nonlinear loops and discuss the relation between these sets and the attractors of the loops. For the canonical H{\'e}non map, a numerical method based on curve fitting is proposed to find a positively invariant set containing the strange attractor. This work can be generalized to find inequality termination conditions for loops with nonlinear assignments",

keywords = "Curve fitting, H{\'e}non map, Positively invariant sets, Program verification",

author = "Liyong Shen and Min Wu and Zhengfeng Yang and Zhenbing Zeng",

year = "2009",

doi = "10.1145/1577190.1577218",

language = "英语",

isbn = "9781605586649",

series = "Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009",

pages = "185--190",

booktitle = "Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009",

note = "2009 Conference on Symbolic Numeric Computation, SNC 2009 ; Conference date: 03-08-2009 Through 05-08-2009",

}

Shen, L, Wu, M, Yang, Z & Zeng, Z 2009, Finding positively invariant sets of a class of nonlinear loops via curve fitting. in Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009. Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009, pp. 185-190, 2009 Conference on Symbolic Numeric Computation, SNC 2009, Kyoto, Japan, 3/08/09. https://doi.org/10.1145/1577190.1577218

Finding positively invariant sets of a class of nonlinear loops via curve fitting. / Shen, Liyong; Wu, Min; Yang, Zhengfeng et al.
Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009. 2009. p. 185-190 (Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Shen, Liyong

AU - Wu, Min

AU - Yang, Zhengfeng

AU - Zeng, Zhenbing

PY - 2009

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N2 - In this paper, we study positively invariant sets of a class of nonlinear loops and discuss the relation between these sets and the attractors of the loops. For the canonical Hénon map, a numerical method based on curve fitting is proposed to find a positively invariant set containing the strange attractor. This work can be generalized to find inequality termination conditions for loops with nonlinear assignments

AB - In this paper, we study positively invariant sets of a class of nonlinear loops and discuss the relation between these sets and the attractors of the loops. For the canonical Hénon map, a numerical method based on curve fitting is proposed to find a positively invariant set containing the strange attractor. This work can be generalized to find inequality termination conditions for loops with nonlinear assignments

KW - Curve fitting

KW - Hénon map

KW - Positively invariant sets

KW - Program verification

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DO - 10.1145/1577190.1577218

M3 - 会议稿件

AN - SCOPUS:70450182145

SN - 9781605586649

T3 - Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009

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BT - Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009

T2 - 2009 Conference on Symbolic Numeric Computation, SNC 2009

Y2 - 3 August 2009 through 5 August 2009

ER -

Finding positively invariant sets of a class of nonlinear loops via curve fitting

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Keywords

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