Numerical Methods for General and Structured Eigenvalue Problems: 46 (Lecture Notes in Computational Science and Engineering, 46) - Image 1

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Springer Numerical Methods for General and Structured Eigenvalue Problems: 46 (Lecture Notes in Computational Science and Engineering, 46)

Name: Numerical Methods for General and Structured Eigenvalue Problems: 46 (Lecture Notes in Computational Science and Engineering, 46)
Brand: Springer
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Computer Science

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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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Brand: Springer
Format: paperback
ASIN: 3540245464
Category: Books > Subjects > Computing & Internet > Computer Science
Domain: Amazon UK
Release Date: 15 July 2005
Listed Since: 10 December 2006

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Springer Numerical Methods for General and Structured Eigenvalue Problems: 46 (Lecture Notes in Computational Science and Engineering, 46)

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Springer Numerical Methods for General and Structured Eigenvalue Problems: 46 (Lecture Notes in Computational Science and Engineering, 46)

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