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Mathematics of Computation

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“Best” interpolation, differentiation, and integration approximations on the Hardy space $H^{2}$

Author: Leon Winslow
Journal: Math. Comp. 24 (1970), 523-527
MSC: Primary 30A78; Secondary 41A50
MathSciNet review: 0293309
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Abstract: A general formula is developed which gives the "best" approximation for any linear functional on the Hardy space ${H^2}$. Some "best" approximations are given for interpolation, differentiation, and integration and are compared to polynomial approximations.

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Keywords: Approximation of linear functionals, best approximations, Hardy space <IMG WIDTH="33" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^2}$">, numerical interpolation, numerical differentiation, numerical integration, analytic functions, approximation by rational functions
Article copyright: © Copyright 1970 American Mathematical Society