bokomslag Numerical Methods for General and Structured Eigenvalue Problems
Vetenskap & teknik

Numerical Methods for General and Structured Eigenvalue Problems

Daniel Kressner

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  • 258 sidor
  • 2005
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].
  • Författare: Daniel Kressner
  • Illustratör: 10 schwarz-weiße Tabellen 32 schwarz-weiße Abbildungen Bibliographie
  • Format: Pocket/Paperback
  • ISBN: 9783540245469
  • Språk: Engelska
  • Antal sidor: 258
  • Utgivningsdatum: 2005-07-01
  • Förlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K