Daniel Kressner 
Numerical Methods for General and Structured Eigenvalue Problems [PDF ebook] 

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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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Table des matières

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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Langue Anglais ● Format PDF ● Pages 258 ● ISBN 9783540285021 ● Taille du fichier 2.8 MB ● Maison d’édition Springer Berlin ● Lieu Heidelberg ● Pays DE ● Publié 2006 ● Téléchargeable 24 mois ● Devise EUR ● ID 2161111 ● Protection contre la copie DRM sociale

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