E-Book (pdf) Numerical Methods for General and Structured Eigenvalue Problems von Daniel Kressner
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This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.



Zusammenfassung
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].

Inhalt
The QR Algorithm.- The QZ Algorithm.- The Krylov-Schur Algorithm.- Structured Eigenvalue Problems.- Background in Control Theory Structured Eigenvalue Problems.- Software.
Titel
Numerical Methods for General and Structured Eigenvalue Problems
Autor
Daniel Kressner
EAN
9783540285021
ISBN
978-3-540-28502-1
Format
E-Book (pdf)
Hersteller
Springer Berlin Heidelberg
Herausgeber
Springer
Veröffentlichung
20.01.2006
Digitaler Kopierschutz
Wasserzeichen
Dateigrösse
2.17 MB
Anzahl Seiten
258
Jahr
2006
Untertitel
Englisch