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Symmetric Hankel operators: minimal norm extensions and eigenstructures
Journal article   Peer reviewed

Symmetric Hankel operators: minimal norm extensions and eigenstructures

J. William Helton and Hugo J. Woerdeman
Linear algebra and its applications, v 185(C)
1993
DOI: https://doi.org/10.1016/0024-3795(93)90201-X
url
https://doi.org/10.1016/0024-3795(93)90201-XView
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Abstract

The minimal norm extension problem for real partial Hankel matrices is studied: Let x i , i ϵ α ⊆ n (= {1,…, n}) be given real numbers. Find x i , i ϵ n \ α, such that the (finite) Hankel matrix (A) H (x)= x 1 x 2 ⋯ x n x 2 x 3 ⋰ 0 ⋮ ⋮ ⋮ x n 0 ⋮ 0 has lowest possible norm (as an operator on the Eucledian space R n ). This min-max problem is reduced to an unconstrained maximization problem. It is close to a nonlinear eigenvalue problem. The results suggest a new class of computer algorithms.

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