Spectral functions for real symmetric Toeplitz matrices
โ Scribed by A. Melman
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 631 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0377-0427
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โฆ Synopsis
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. (~) 1998 Elsevier Science B.V. All rights reserved.
๐ SIMILAR VOLUMES
If n t rรs n rYs0 is a real symmetric Toeplitz (RST) matrix then R n has a basis consisting of dna2e eigenvectors x satisfying (A) tx x and na2 eigenvectors y satisfying (B) ty รy, where t is the ยฏip matrix. We say that an eigenvalue k of n is even if a k-eigenvector of n satisยฎes (A), or odd if a k
## Abstract Split Levinson and Schur algorithms for the inversion of symmetric Toeplitz matrices are presented that work, in contrast to previous algorithms, without additional conditions like strong nonโsingularity. Copyright ยฉ 2004 John Wiley & Sons, Ltd.