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Numerical Methods for General and Structured Eigenvalue Problems

Medium: Buch
ISBN: 978-3-540-24546-9
Verlag: Springer
Erscheinungstermin: 15.07.2005
Lieferfrist: bis zu 10 Tage

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].


Produkteigenschaften


  • Artikelnummer: 9783540245469
  • Medium: Buch
  • ISBN: 978-3-540-24546-9
  • Verlag: Springer
  • Erscheinungstermin: 15.07.2005
  • Sprache(n): Englisch
  • Auflage: 1. Auflage 2005
  • Serie: Lecture Notes in Computational Science and Engineering
  • Produktform: Kartoniert
  • Gewicht: 880 g
  • Seiten: 258
  • Format (B x H): 155 x 235 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

The QR Algorithm.- The QZ Algorithm.- The Krylov-Schur Algorithm.- Structured Eigenvalue Problems.- Background in Control Theory Structured Eigenvalue Problems.- Software.