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
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813