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Conditioning of infinite Hankel matrices of finite rank

✍ Scribed by F.S.V. Bazán; Ph.L. Toint

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
207 KB
Volume
41
Category
Article
ISSN
0167-6911

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✦ Synopsis

Let H be an inÿnite Hankel matrix with hi+j-2 as its (i; j)-entry, h k = n l=1 r l z k l , k = 0; 1; : : : ; |z l | ¡ 1, and r l ; z l ∈ C. We derive upper bounds for the 2-condition number of H as functions of n, r l and z l , which show that the Hankel matrix H becomes well conditioned whenever the z's are close to the unit circle but not extremely close to each other. Numerical results which illustrate the theory are provided.

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