Numerical Methods for General and Structured Eigenvalue Problems [electronic resource] /
by Daniel Kressner.
- XIV, 258 p. 32 illus. online resource.
- Lecture Notes in Computational Science and Engineering, 46 1439-7358 ; .
- Lecture Notes in Computational Science and Engineering, 46 .
The QR Algorithm -- The QZ Algorithm -- The Krylov-Schur Algorithm -- Structured Eigenvalue Problems -- Background in Control Theory Structured Eigenvalue Problems -- Software.
ZDB-2-SMA
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].
9783540285021
10.1007/3-540-28502-4 doi
Mathematics. Systems theory. Computer science--Mathematics. Computer science. Mathematics. Computational Mathematics and Numerical Analysis. Systems Theory, Control. Computational Science and Engineering.