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Numerical Methods for General and Structured Eigenvalue Problems by Daniel Kressner

Numerical Methods for General and Structured Eigenvalue Problems

by Daniel Kressner
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Book cover type: Paperback
  • ISBN13: 9783540245469
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 258
  • Original Price: EUR 99.99
  • Language: English
  • Edition: 2005
  • Item Weight: 427 grams
  • BISAC Subject(s): Number Systems, Applied, and Counting & Numeration

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].

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