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### Nonnegative \(C^2\) interpolation

**Student-Run Applied & Math Seminar**

Speaker: | Fushuai "Black" Jiang, UC Davis |

Location: | 3106 MSB |

Start time: | Thu, Jan 17 2019, 12:30PM |

In this talk, we consider the following extension problem of Whitney-type:

Supposed we are given a finite planar set with prescribed nonnegative values on this set. How do we decide the minimal \(C^2\) norm of all the globally nonnegative twice continuously differentiable functions (within an order of magnitude) that interpolate these values?

We hope to provide a two-fold answer. First, we want to come up with an algorithm to calculate the minimal norm. Second, we want a find a procedure to recover an interpolant that witnesses the minimal norm.

This is a joint work with Professor Kevin Luli.