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Titlebook: Nonlinear Numerical Methods and Rational Approximation; Annie Cuyt Book 1988 D. Reidel Publishing Company, Dordrecht, Holland 1988 Hyperge

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On the Behavior of Zeros and Poles of Best Uniform Polynomial and Rational Approximantson E̊, but not on E. Our results are related to a recent theorem of Blatt, Saff, and Simkani which roughly states that the zeros of a . of best polynomial approximants distribute like the equilibrium measure for E. In contrast, we show that there might be another subsequence with zeros essentially a
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Once Again: The Adamjan-Arov-Krein Approximation Theoryptimal Hankel-norm approximation for . multivariable systems of finite degree. A special emphasis is laid on the rationale for the Hankel-matrix approach and on the singular value decomposition of bounded infinite Hankel matrices of finite rank (with some original matrix-theoretic complements). Amon
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Simultaneous Rational Approximation to Some q-Hypergeometric Functionsric .......) functions to so called basic q-hypergeometric functions of the same type, including explicit formulae for the last two types mentioned. Appropriate changes of the variable and/or taking the limit for . → 1 show that the results include known results on both ordinary (cf. P. Wynn) and si
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Minimal Pade-Sense Matrix Approximations Around , = 0 and , = ∞ystem theory, the minimal partial realization problem with Markov parameters and time moments. It gives a solution in the form of a polynomial matrix fraction. The algorithm is a generalization of the Berlekamp-Massey algorithm for the scalar case [1,2,7]. Our approach is mainly based on the work of
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Some Orthogonal Systems of p+1Fp-Type Laurent Polynomials polynomials on the unit circle in C with respect to the weight function w(z) = const.(-z).(1-z). a,c∈ ., c>a, we get orthogonal systems of .F.-type Laurent polynomials by adding linear combinations of the delta function δ. at the point 1 and its first ρ derivatives to the weight function w..If only
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