Impossibility of Approximating Analytic Functions from Equispaced Samples
نویسنده
چکیده
It is shown that no stable procedure for approximating functions from equally spaced samples can converge geometrically for analytic functions. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992. In a nutshell, you can't beat Gibbs and Runge. Monday December 14 2009 4:30 PM Building 4, Room 370 Refreshments are available in Building 2, Room 290 (Math Common Room) between 3:30 – 4:30 PM Applied Math Colloquium: http://math.mit.edu/amc/fall09 Math Department: http://www-math.mit.edu To sign up for Applied Mathematics Colloquium announcements, please contact [email protected] Massachusetts Institute of Technology Department of Mathematics Cambridge, MA 02139
منابع مشابه
Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992.
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