Remarks on extreme eigenvalues of Toeplitz matrices

Mohsen Pourahmadi

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-4

Abstract:

Let f be a nonnegative integrable function on [ − π , π ] , T n ( f ) the ( n + 1 ) × ( n + 1 ) Toeplitz matrix associated with f and λ 1 , n its smallest eigenvalue. It is shown that the convergence of λ 1 , n to min f ( 0 ) can be exponentially fast even when f does not satisfy the smoothness condition of Kac, Murdoch and Szegö (1953). Also a lower bound for λ 1 , n corresponding to a large class of functions which do not satisfy this smoothness condition is provided.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:686413

DOI: 10.1155/S0161171288000055

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