Outer Interval Solution of the Eigenvalue Problem under General Form Parametric Dependencies

Outer Interval Solution of the Eigenvalue Problem under General Form Parametric Dependencies The paper addresses the problem of determining an outer interval solution of the parametric eigenvalue problem A(p)x = λx, A(p) ∈ ℝn×n for the general case where the matrix elements a ij(p) are continuous nonlinear functions of the parameter vector p, p belonging to the interval vector p. A method for computing an interval enclosure of each eigenpair (λμ, x (μ)), μ = 1, ..., n, is suggested for the case where λμ is a simple eigenvalue. It is based on the use of an affine interval approximation of a ij (p) in p and reduces, essentially, to setting up and solving a real system of n or 2n incomplete quadratic equations for each real or complex eigenvalue, respectively. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Outer Interval Solution of the Eigenvalue Problem under General Form Parametric Dependencies

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2006 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-006-4875-1
Publisher site
See Article on Publisher Site

Abstract

The paper addresses the problem of determining an outer interval solution of the parametric eigenvalue problem A(p)x = λx, A(p) ∈ ℝn×n for the general case where the matrix elements a ij(p) are continuous nonlinear functions of the parameter vector p, p belonging to the interval vector p. A method for computing an interval enclosure of each eigenpair (λμ, x (μ)), μ = 1, ..., n, is suggested for the case where λμ is a simple eigenvalue. It is based on the use of an affine interval approximation of a ij (p) in p and reduces, essentially, to setting up and solving a real system of n or 2n incomplete quadratic equations for each real or complex eigenvalue, respectively.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

References

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