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- W2069133426 abstract "For a rational matrix function Φ with poles outside the unit circle, we estimate the degree of the unique superoptimal approximation AΦ by matrix functions analytic in the unit disk. We obtain sharp estimates in the case of 2 x 2 matrix functions. It turns out that generically deg AΦ ≤ degΦ - 2. We prove that for an arbitrary 2 x 2 rational function Φ, degAΦ ≤ 2degΦ - 3 whenever degΦ ≥ 2. On the other hand, for k ≥ 2, we construct a 2 x 2 matrix function Φ, for which degΦ = k, while deg AΦ = 2k-3. Moreover, we conduct a detailed analysis of the situation when the inequality deg AΦ ≤ degΦ-2 can violate and obtain best possible results." @default.
- W2069133426 created "2016-06-24" @default.
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- W2069133426 date "2007-01-01" @default.
- W2069133426 modified "2023-10-18" @default.
- W2069133426 title "Analytic approximation of rational matrix functions" @default.
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- W2069133426 doi "https://doi.org/10.1512/iumj.2007.56.3075" @default.
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