Numerical Methods for General and Structured Eigenvalue Problems

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(...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Kressner, Daniel (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
Σειρά:Lecture Notes in Computational Science and Engineering, 46
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Kressner, Daniel.  |e author. 
245 1 0 |a Numerical Methods for General and Structured Eigenvalue Problems  |h [electronic resource] /  |c by Daniel Kressner. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg,  |c 2005. 
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490 1 |a Lecture Notes in Computational Science and Engineering,  |x 1439-7358 ;  |v 46 
505 0 |a The QR Algorithm -- The QZ Algorithm -- The Krylov-Schur Algorithm -- Structured Eigenvalue Problems -- Background in Control Theory Structured Eigenvalue Problems -- Software. 
520 |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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650 0 |a System theory. 
650 0 |a Computer mathematics. 
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650 2 4 |a Systems Theory, Control. 
650 2 4 |a Computational Science and Engineering. 
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830 0 |a Lecture Notes in Computational Science and Engineering,  |x 1439-7358 ;  |v 46 
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