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• W2169088502 abstract "Abstract Let G be a matrix function of type m × n and suppose that G is expressible as the sum of an H ∞ function and a continuous function on the unit circle. Suppose also that the ( k – 1)th singular value of the Hankel operator with symbol G is greater than the k th singular value. Then there is a unique superoptimal approximant to G in : that is, there is a unique matrix function Q having at most k poles in the open unit disc which minimizes s ∞ ( G – Q ) or, in other words, which minimizes the sequence with respect to the lexicographic ordering, where and S j (·) denotes the j th singular value of a matrix. This result is due to the present authors [ PY1 ] in the case k = 0 (when the hypothesis on the Hankel singular values is vacuous) and to S. Treil[ T2 ] in general. In this paper we give a proof of uniqueness by a diagonalization argument, a high level algorithm for the computation of the superoptimal approximant and a recursive parametrization of the set of all optimal solutions of a matrix Nehari—Takagi problem." @default.
• W2169088502 created "2016-06-24" @default.
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• W2169088502 date "1996-04-01" @default.
• W2169088502 modified "2023-09-27" @default.
• W2169088502 title "Superoptimal approximation by meromorphic functions" @default.
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• W2169088502 doi "https://doi.org/10.1017/s0305004100074375" @default.
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