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Polynomials Gone Wild
Alexander Bilik
Mathematics Department, UCSD
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 19, 2008
11:00AM AP&M 2402
Alexander Bilik
Mathematics Department, UCSD
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 19, 2008
11:00AM AP&M 2402