Tata Institute of Fundamental Research
Weierstrass Polynomial Approximation Theorem for $C[0,1]$ via Weak Law of Large Numbers
STCS Seminar
Speaker:
Krishna Athreya (Iowa State University
Department of Statistics
2438 Osborn Dr. Ames
Iowa 50011-4040
United States of America)
Organiser:
Sandeep K Juneja
Date:
Monday, 25 Jul 2016, 16:00 to 17:00
Venue:
A-201 (STCS Seminar Room)
(Scan to add to calendar)
Abstract:
Karl Weierstrass showed that given a continuous function $f$ on $[0,1]$ and an epsilon positive, there is a polynomial $p$ such that it is uniformly epsilon close to $f$ on $[0,1]$. In this talk we give a proof of this using coin tossing. We then generalize this to the case of simplexes and hypercubes. We also discuss approximation by $C^{\infty}$ infinity functions using Gauss kernels.
| Speaker: | Krishna Athreya (Iowa State University Department of Statistics 2438 Osborn Dr. Ames Iowa 50011-4040 United States of America) |
| Organiser: | Sandeep K Juneja |
| Date: | Monday, 25 Jul 2016, 16:00 to 17:00 |
| Venue: | A-201 (STCS Seminar Room) |
(Scan to add to calendar)
Abstract:
Karl Weierstrass showed that given a continuous function $f$ on $[0,1]$ and an epsilon positive, there is a polynomial $p$ such that it is uniformly epsilon close to $f$ on $[0,1]$. In this talk we give a proof of this using coin tossing. We then generalize this to the case of simplexes and hypercubes. We also discuss approximation by $C^{\infty}$ infinity functions using Gauss kernels.