Abstract
Given a vector of functions f = (f o,…, f m), with each analytic in an open set D
containing the origin, 0 ≤ j ≤ m, the relationship between Hermite-Padé polynomials of Type I and Type II is examined. A best simultaneous rational approximant for f on any compact subset K of D is defined, and we prove that when the error in best simultaneous rational approximation tends to zero faster than geometrically, certain sequences of Hermite-Padé Type I and Type II approximants to f converge in capacity.
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© 1994 Springer Science+Business Media Dordrecht
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Driver, K.A., Lubinsky, D.S., Wallin, H. (1994). Hermite-Padé Polynomials and Approximation Properties. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_22
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DOI: https://doi.org/10.1007/978-94-011-0970-3_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4420-2
Online ISBN: 978-94-011-0970-3
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