Sökning: L773:0024 3795 OR L773:1873 1856
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Polynomial two-para...
Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
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- Jarlebring, Elias (författare)
- Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Belgium
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- Hochstenbach, M.E. (författare)
- Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
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(creator_code:org_t)
- Elsevier BV, 2009
- 2009
- Engelska.
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 431:3-4, s. 369-380
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Abstract
Ämnesord
Stäng
- Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called matrix pencil methods, the general ideas used as well as the proofs differ considerably. Moreover, the available theory hardly reveals the relations between the different methods. In this work, a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem: the polynomial two-parameter eigenvalue problem, of which the quadratic two-parameter eigenvalue problem is a special case. This framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods. We also recognize a few new matrix pencil variants to determine DDE stability. Finally, the recognition of the new types of eigenvalue problem opens a door to efficient computation of DDE stability. (C) 2009 Elsevier Inc. All rights reserved.
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
Nyckelord
- Delay-differential equations; Two-parameter eigenvalue problem; Multiparameter eigenvalue problem; Critical delays; Robustness; Stability; Asymptotic stability; Companion form; Quadratic eigenvalue problem; Polynomial eigenvalue problem; Quadratic two-parameter eigenvalue problem; Polynomial two-parameter eigenvalue problem
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