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Shifted Fourier Matrices and Their Tridiagonal Commutors
SIAM Journal on Matrix Analysis and Applications, 2003Let \(n\) be a positive integer, and let \(\tau \) and \(\alpha \) be complex constants. As abbreviations, let \(m=(n-1)/2\) and \(a=\alpha /\tau \) (if \(\tau \neq 0\)). We define two forms of the shifted Fourier matrix specified by these parameters. The first form (the periodic form) is the \(n\times n\) matrix \[ \widetilde{F}_{n}\left( \tau ,\alpha
Clary, Stuart, Mugler, Dale H.
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Tridiagonal Toeplitz matrices: properties and novel applications
Numerical Linear Algebra with Applications, 2012SUMMARYThe eigenvalues and eigenvectors of tridiagonal Toeplitz matrices are known in closed form. This property is in the first part of the paper used to investigate the sensitivity of the spectrum. Explicit expressions for the structured distance to the closest normal matrix, the departure from normality, and theϵ‐pseudospectrum are derived.
NOSCHESE, Silvia +2 more
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Sturm Sequences of Tridiagonal Matrices
1993The contents of this chapter is, in a sense, central for the whole book. The two—side Sturm sequences, the algorithms of construction of whose are presented here, are used to construct the orthogonal transformations in deflation algorithms for band matrices.
S. K. Godunov +3 more
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Regular Domains of Tridiagonal Matrices
1988Many numerical problems are related to the study of the regularities of tridiagonal matrices. Recently, a series of sharp conditions for such matrices to be regular have been obtained through geometrical considerations and use of an associated three-term recurrence relation.
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On Lanczos’ Algorithm for Tridiagonalizing Matrices
SIAM Review, 1961Causey, R. L., Gregory, R. T.
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Tridiagonal M-matrices with tridiagonal Moore-Penrose inverse
Applied Mathematics and ComputationM.I. Bueno +3 more
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A Family of Tridiagonal Matrices
The Fibonacci Quarterly, 1978Gerald E. Bergum, Verner E. Hoggatt
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