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Tridiagonal Toeplitz matrices: properties and novel applications

Authors


  • Dedicated to Biswa N. Datta on the occasion of his 70th birthday.

Correspondence to: Lothar Reichel, Department of Mathematical Sciences, Kent State University, Kent, OH 44242, U.S.A.

E-mail: reichel@math.kent.edu

SUMMARY

The 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 the ϵ-pseudospectrum are derived. The second part of the paper discusses applications of the theory to inverse eigenvalue problems, the construction of Chebyshev polynomial-based Krylov subspace bases, and Tikhonov regularization. Copyright © 2012 John Wiley & Sons, Ltd.

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