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Remarks on extreme eigenvalues of Toeplitz matrices

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  • Mohsen Pourahmadi

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.

Suggested Citation

  • Mohsen Pourahmadi, 1988. "Remarks on extreme eigenvalues of Toeplitz matrices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:686413
    DOI: 10.1155/S0161171288000055
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