Spectral functions for real symmetric Toeplitz matrices
نویسندگان
چکیده
منابع مشابه
Spectral Functions for Real Symmetric Toeplitz Matrices
We derive separate spectral functions for the even and odd spectra of a real symmetric Toeplitz matrix, which are given by the roots of those functions. These are rational functions, also commonly referred to as secular functions. Two applications are considered: spectral evolution as a function of one parameter and the computation of eigenvalues.
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We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.
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We derive upper and lower bounds on the smallest and largest eigenvalues, respectively, of real symmetric Toeplitz matrices. The bounds are rst obtained for positive-deenite matrices and then extended to the general real symmetric case. Our bounds are computed as the roots of rational and polynomial approximations to spectral, or secular, equations. The decomposition of the spectrum into even a...
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Abstract How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable structure. In this paper, we proved that the symmetric Toeplitz matrix and its transforms can be used as measurement matrix and recovery signal with high p...
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In regard to the linear subspace T (n) of n n symmetric Toeplitz matrices over the real eld, the collection S(n) of all real and orthogonal matrices Q such that QTQT 2 T (n) whenever T 2 T (n) forms a group, called the stability group of T (n). This paper shows that S(n) is nite. In fact, S(n) has exactly eight elements regardless of the dimension n. Group elements in S(n) are completely charac...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00129-0