E Book

Numerical Methods for General and Structured Eigenvalue Problems

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

Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

Berlin, Heidelberg : Springer., 2005

Deskripsi Fisik

XIV, 258 p. 32 illus.online resource.

Bahasa

English

ISBN/ISSN

9783540285021

Klasifikasi

518

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

1st ed. 2005.

Subjek

Computer mathematics.
Computational Science and Engineering.
System theory.
Systems Theory, Control.
Computational Mathematics and Numerical Analysis.

Info Detail Spesifik

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Pernyataan Tanggungjawab

Daniel Kressner.

Versi lain/terkait

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