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03062nam a22004695i 4500 |
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978-3-540-28502-1 |
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|a 9783540285021
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|a 10.1007/3-540-28502-4
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|a Kressner, Daniel.
|e author.
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|a Numerical Methods for General and Structured Eigenvalue Problems
|h [electronic resource] /
|c by Daniel Kressner.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2005.
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|a XIV, 258 p. 32 illus.
|b online resource.
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|a text
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|a Lecture Notes in Computational Science and Engineering,
|x 1439-7358 ;
|v 46
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|a The QR Algorithm -- The QZ Algorithm -- The Krylov-Schur Algorithm -- Structured Eigenvalue Problems -- Background in Control Theory Structured Eigenvalue Problems -- Software.
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|a The purpose of this book is to describe recent developments in solving eig- value problems, in particular with respect to the QR and QZ algorithms as well as structured matrices. Outline Mathematically speaking, the eigenvalues of a square matrix A are the roots of its characteristic polynomial det(A??I). An invariant subspace is a linear subspace that stays invariant under the action of A. In realistic applications, it usually takes a long process of simpli?cations, linearizations and discreti- tions before one comes up with the problem of computing the eigenvalues of a matrix. In some cases, the eigenvalues have an intrinsic meaning, e.g., for the expected long-time behavior of a dynamical system; in others they are just meaningless intermediate values of a computational method. The same applies to invariant subspaces, which for example can describe sets of initial states for which a dynamical system produces exponentially decaying states. Computing eigenvalues has a long history, dating back to at least 1846 when Jacobi [172] wrote his famous paper on solving symmetric eigenvalue problems. Detailed historical accounts of this subject can be found in two papers by Golub and van der Vorst [140, 327].
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|a Mathematics.
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|a System theory.
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|a Computer mathematics.
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|a Mathematics.
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|a Computational Mathematics and Numerical Analysis.
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|a Systems Theory, Control.
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|a Computational Science and Engineering.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783540245469
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|a Lecture Notes in Computational Science and Engineering,
|x 1439-7358 ;
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|u http://dx.doi.org/10.1007/3-540-28502-4
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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