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Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst

Administrative Contact:
Terry Le

Office: AP&M 7431
Phone: (858)534-9813
Fax: (858)534-5273
E-mail: tele@ucsd.edu
Polynomials Gone Wild

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Abstract:

It is well known that polynomials are dense in thecontinuous functions, so that given a continuous function, a uniformlyconvergent sequence of polynomials exists. However, in choosing nodesto approximate functions, it often happens that one must choose thenodes before knowing the functions. So is there a sequence of nodessuch that, for any function, the interpolating polynomials uniformlyconverge to the function? Sadly, the answer is no. I will prove this,and also discuss various related results.

Monday, May 26, 2008
11:00AM AP&M 2402