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130626 ||| eng |
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|a 9783540285021
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|a Kressner, Daniel
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|a Numerical Methods for General and Structured Eigenvalue Problems
|h Elektronische Ressource
|c by Daniel Kressner
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| 250 |
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|a 1st ed. 2005
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2005, 2005
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| 300 |
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|a XIV, 258 p. 32 illus
|b online resource
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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 Computational Mathematics and Numerical Analysis
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| 653 |
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|a Mathematics / Data processing
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| 653 |
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|a Control theory
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| 653 |
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|a Systems Theory, Control
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| 653 |
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|a Computational Science and Engineering
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| 653 |
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|a System theory
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|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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|a Lecture Notes in Computational Science and Engineering
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|a 10.1007/3-540-28502-4
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|u https://doi.org/10.1007/3-540-28502-4?nosfx=y
|x Verlag
|3 Volltext
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|a 518
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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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