For more information about this meeting, contact Svetlana Katok, Stephanie Zerby, Flossie Dunlop.

Title: | Being right more often can make you more wrong |

Seminar: | PMASS Colloquium |

Speaker: | John Roe, The Pennsylvania State University |

Abstract: |

Suppose that we know the values of a function f(x) at (n+1) different x-values, say in the interval [0,1]. A polynomial function p(x), of degree n, can be put through these (n+1) points and it is natural to use p as an approximation to f for other x-values also. This idea, called "polynomial collocation", is one of the oldest in numerical analysis.
I'll explain some of the techniques that were used in the B.C. (=before computer) era to carry out these calculations using pencil and paper. Then, I'll show you a surprising fact: as n increases (so that the number of points at which the approximation is "right" gets larger), the difference between p(x) and f(x) for other x-values can increase without bound. In brief, being right more often can make you more wrong. |

### Room Reservation Information

Room Number: | MB113 |

Date: | 04 / 05 / 2012 |

Time: | 02:30pm - 03:30pm |