Aug 19, 2017

Jane works for for a famous bioinformatics company.

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Jane works for for a famous bioinformatics company. Last year she was required by Management to approximate an important but complicated formula, g(x), defined on the interval [−1,1], by a polynomial of degree n +1. She did so, and called the result f (x) = pn+1(x). Last week, Management decided that they really needed a polynomial of degree n, not n +1, to represent g. Alas, the original g had been lost by this time and all that was left was f (x). Therefore, Jane is looking for the polynomial of degree n which is closest (in the maximum norm) to f on the interval [−1,1]. Please help her find it.

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