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＜電子ブック＞
Numerical Methods for General and Structured Eigenvalue Problems / by Daniel Kressner
(Lecture Notes in Computational Science and Engineering. ISSN:21977100 ; 46)

版	1st ed. 2005.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	XIV, 258 p. 32 illus : online resource
著者標目	*Kressner, Daniel author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:System theory LCSH:Control theory FREE:Computational Mathematics and Numerical Analysis FREE:Systems Theory, Control FREE:Computational Science and Engineering
一般注記	The QR Algorithm -- The QZ Algorithm -- The Krylov-Schur Algorithm -- Structured Eigenvalue Problems -- Background in Control Theory Structured Eigenvalue Problems -- Software 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] HTTP:URL=https://doi.org/10.1007/3-540-28502-4

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