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Inverse Eigenvalue ProblemsTheory, Algorithms, and Applications$
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Moody Chu and Gene Golub

Print publication date: 2005

Print ISBN-13: 9780198566649

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566649.001.0001

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SPECTRALLY CONSTRAINED APPROXIMATION

SPECTRALLY CONSTRAINED APPROXIMATION

Chapter:
(p.212) 7 SPECTRALLY CONSTRAINED APPROXIMATION
Source:
Inverse Eigenvalue Problems
Author(s):

Moody T. Chu

Gene H. Golub

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566649.003.0007

This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general framework by using the projected gradient method is described. A broad range of applications, including the Toeplitz inverse eigenvalue problem, the simultaneous reduction problem, and the nearest normal matrix approximation, are discussed.

Keywords:   spectrally constrained optimization, projected gradient, Toeplitz inverse eigenvalue, simultaneous reduction, nearest matrix approximation

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