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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