Article

Computing the cube of an interval matrix is NP-Hard

Authors:

Olga Kosheleva,

Vladik Kreinovich,

Hung T. NguyenAuthors Info & Claims

SAC '05: Proceedings of the 2005 ACM symposium on Applied computing

Pages 1449 - 1453

https://doi.org/10.1145/1066677.1067007

Published: 13 March 2005 Publication History

Abstract

In many practical applications, we are interested in computing the product of given matrices and/or a power of a given matrix. In some cases, the initial matrices are only known with interval uncertainty. It turns out that under this uncertainty, there is a principal difference between the product of two matrices and the product of three (or more) matrices:• on the one hand, it is more or less known that the problems of computing the exact range for the product of two matrices - and for the square of a matrix - are computationally feasible;• on the other hand, we prove that the problems of computing the exact ranges for the product of three matrices - and for the third power of a matrix - are NP-hard.

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Cited By

Forets MFreire DSchilling C(2020)Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions2020 18th ACM-IEEE International Conference on Formal Methods and Models for System Design (MEMOCODE)10.1109/MEMOCODE51338.2020.9314994(1-6)Online publication date: 2-Dec-2020
https://doi.org/10.1109/MEMOCODE51338.2020.9314994
Jacek Kubica B(2020)Interval Methods for Solving Various Kinds of Quantified Nonlinear ProblemsBeyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications10.1007/978-3-030-31041-7_17(311-328)Online publication date: 29-Feb-2020
https://doi.org/10.1007/978-3-030-31041-7_17
Schulze Darup M(2016)Rigorous constraint satisfaction for sampled linear systemsEuropean Journal of Control10.1016/j.ejcon.2016.06.00331(52-58)Online publication date: Sep-2016
https://doi.org/10.1016/j.ejcon.2016.06.003
Show More Cited By

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Computing the cube of an interval matrix is NP-Hard

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Published In

cover image ACM Conferences

SAC '05: Proceedings of the 2005 ACM symposium on Applied computing

March 2005

1814 pages

ISBN:1581139640

DOI:10.1145/1066677

Conference Chair:
Hisham M. Haddad
Kennesaw State University
,
Editor:
Lorie M. Liebrock
New Mexico Institute of Mining and Technology, Socorro, NM
,
Program Chairs:
Andrea Omicini
Alma Mater Studiorum, Universita di Bologna, Italy
,
Roger L. Wainwright
Univerity of Tulsa, OK

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

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Published: 13 March 2005

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SAC05: The 2005 ACM Symposium on Applied Computing

March 13 - 17, 2005

New Mexico, Santa Fe

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Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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Cited By

Forets MFreire DSchilling C(2020)Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions2020 18th ACM-IEEE International Conference on Formal Methods and Models for System Design (MEMOCODE)10.1109/MEMOCODE51338.2020.9314994(1-6)Online publication date: 2-Dec-2020
https://doi.org/10.1109/MEMOCODE51338.2020.9314994
Jacek Kubica B(2020)Interval Methods for Solving Various Kinds of Quantified Nonlinear ProblemsBeyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications10.1007/978-3-030-31041-7_17(311-328)Online publication date: 29-Feb-2020
https://doi.org/10.1007/978-3-030-31041-7_17
Schulze Darup M(2016)Rigorous constraint satisfaction for sampled linear systemsEuropean Journal of Control10.1016/j.ejcon.2016.06.00331(52-58)Online publication date: Sep-2016
https://doi.org/10.1016/j.ejcon.2016.06.003
Althoff MKrogh BStursberg O(2011)Analyzing Reachability of Linear Dynamic Systems with Parametric UncertaintiesModeling, Design, and Simulation of Systems with Uncertainties10.1007/978-3-642-15956-5_4(69-94)Online publication date: 13-May-2011
https://doi.org/10.1007/978-3-642-15956-5_4
Pang CLur Y(2008)On the Stability of Takagi–Sugeno Fuzzy Systems With Time-Varying UncertaintiesIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2007.89595516:1(162-170)Online publication date: 1-Feb-2008
https://dl.acm.org/doi/10.1109/TFUZZ.2007.895955
Althoff MStursberg OBuss M(2007)Reachability analysis of linear systems with uncertain parameters and inputs2007 46th IEEE Conference on Decision and Control10.1109/CDC.2007.4434084(726-732)Online publication date: Dec-2007
https://doi.org/10.1109/CDC.2007.4434084
Ahn HChen YMoore K(2006)Maximum singular value and power of an interval matrix2006 International Conference on Mechatronics and Automation10.1109/ICMA.2006.257671(678-683)Online publication date: Dec-2006
https://doi.org/10.1109/ICMA.2006.257671

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