TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Numerical Methods for General and Structured Eigenvalue Problems
T2  - Lecture Notes in Computational Science and Engineering,
SN  - 9783540285021
AV  - QA71-90 
U1  - 518 23
PY  - 2005///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Systems theory
KW  - Computer science
KW  - Computational Mathematics and Numerical Analysis
KW  - Systems Theory, Control
KW  - Computational Science and Engineering
N1  - The QR Algorithm -- The QZ Algorithm -- The Krylov-Schur Algorithm -- Structured Eigenvalue Problems -- Background in Control Theory Structured Eigenvalue Problems -- Software; ZDB-2-SMA
N2  - 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]
UR  - http://dx.doi.org/10.1007/3-540-28502-4
ER  -