Real root isolation of multi-exponential polynomials with application

Ming Xu; Liangyu Chen; Zhenbing Zeng; Zhi Bin Li

doi:10.1007/978-3-642-11440-3_24

Real root isolation of multi-exponential polynomials with application

Ming Xu^*
, Liangyu Chen
, Zhenbing Zeng
, Zhi Bin Li

^*Corresponding author for this work

East China Normal University

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

1 Scopus citations

Abstract

Real root isolation problem is to compute a list of disjoint intervals, each containing a distinct real root and together containing all. Traditional methods and tools often attack the root isolation for ordinary polynomials. However many other complex systems in engineering are modeling with non-ordinary polynomials. In this paper, we extend the pseudo-derivative sequences and Budan-Fourier theorem for multi-exponential polynomials to estimate the bounds and counts of all real roots. Furthermore we present an efficient algorithm for isolating all real roots under given minimum root separation. As a proof of serviceability, the reachability of linear systems with real eigenvalues only is approximately computable by this algorithm.

Original language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings
Pages	263-268
Number of pages	6
DOIs	https://doi.org/10.1007/978-3-642-11440-3_24
State	Published - 2010
Event	4th International Workshop on Algorithms and Computation, WALCOM 2010 - Dhaka, Bangladesh Duration: 10 Feb 2010 → 12 Feb 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5942 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Workshop on Algorithms and Computation, WALCOM 2010
Country/Territory	Bangladesh
City	Dhaka
Period	10/02/10 → 12/02/10

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10.1007/978-3-642-11440-3_24

Cite this

Xu, M., Chen, L., Zeng, Z., & Li, Z. B. (2010). Real root isolation of multi-exponential polynomials with application. In WALCOM: Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings (pp. 263-268). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5942 LNCS). https://doi.org/10.1007/978-3-642-11440-3_24

@inproceedings{34c00437ac6b4e7d93061cf3d63fd875,

title = "Real root isolation of multi-exponential polynomials with application",

abstract = "Real root isolation problem is to compute a list of disjoint intervals, each containing a distinct real root and together containing all. Traditional methods and tools often attack the root isolation for ordinary polynomials. However many other complex systems in engineering are modeling with non-ordinary polynomials. In this paper, we extend the pseudo-derivative sequences and Budan-Fourier theorem for multi-exponential polynomials to estimate the bounds and counts of all real roots. Furthermore we present an efficient algorithm for isolating all real roots under given minimum root separation. As a proof of serviceability, the reachability of linear systems with real eigenvalues only is approximately computable by this algorithm.",

author = "Ming Xu and Liangyu Chen and Zhenbing Zeng and Li, \{Zhi Bin\}",

year = "2010",

doi = "10.1007/978-3-642-11440-3\_24",

language = "英语",

isbn = "3642114393",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "263--268",

booktitle = "WALCOM",

note = "4th International Workshop on Algorithms and Computation, WALCOM 2010 ; Conference date: 10-02-2010 Through 12-02-2010",

}

Xu, M, Chen, L, Zeng, Z & Li, ZB 2010, Real root isolation of multi-exponential polynomials with application. in WALCOM: Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5942 LNCS, pp. 263-268, 4th International Workshop on Algorithms and Computation, WALCOM 2010, Dhaka, Bangladesh, 10/02/10. https://doi.org/10.1007/978-3-642-11440-3_24

Real root isolation of multi-exponential polynomials with application. / Xu, Ming; Chen, Liangyu; Zeng, Zhenbing et al.
WALCOM: Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings. 2010. p. 263-268 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5942 LNCS).

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

TY - GEN

T1 - Real root isolation of multi-exponential polynomials with application

AU - Xu, Ming

AU - Chen, Liangyu

AU - Zeng, Zhenbing

AU - Li, Zhi Bin

PY - 2010

Y1 - 2010

N2 - Real root isolation problem is to compute a list of disjoint intervals, each containing a distinct real root and together containing all. Traditional methods and tools often attack the root isolation for ordinary polynomials. However many other complex systems in engineering are modeling with non-ordinary polynomials. In this paper, we extend the pseudo-derivative sequences and Budan-Fourier theorem for multi-exponential polynomials to estimate the bounds and counts of all real roots. Furthermore we present an efficient algorithm for isolating all real roots under given minimum root separation. As a proof of serviceability, the reachability of linear systems with real eigenvalues only is approximately computable by this algorithm.

AB - Real root isolation problem is to compute a list of disjoint intervals, each containing a distinct real root and together containing all. Traditional methods and tools often attack the root isolation for ordinary polynomials. However many other complex systems in engineering are modeling with non-ordinary polynomials. In this paper, we extend the pseudo-derivative sequences and Budan-Fourier theorem for multi-exponential polynomials to estimate the bounds and counts of all real roots. Furthermore we present an efficient algorithm for isolating all real roots under given minimum root separation. As a proof of serviceability, the reachability of linear systems with real eigenvalues only is approximately computable by this algorithm.

UR - https://www.scopus.com/pages/publications/77949590410

U2 - 10.1007/978-3-642-11440-3_24

DO - 10.1007/978-3-642-11440-3_24

M3 - 会议稿件

AN - SCOPUS:77949590410

SN - 3642114393

SN - 9783642114397

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 263

EP - 268

BT - WALCOM

T2 - 4th International Workshop on Algorithms and Computation, WALCOM 2010

Y2 - 10 February 2010 through 12 February 2010

ER -

Xu M, Chen L, Zeng Z, Li ZB. Real root isolation of multi-exponential polynomials with application. In WALCOM: Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings. 2010. p. 263-268. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-11440-3_24

Real root isolation of multi-exponential polynomials with application

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