[ugrads] Invitation for the Comprehensive Exam for Xuan Zhou

Myrna Walker mwalke13 at iit.edu
Fri Mar 28 11:35:45 CDT 2014


Please note the correct title.

"TRACTABILITY AND ERROR ESTIMATION OF RADIAL BASIS FUNCTION APPROXIMATION".

Thanks.
Myrna


On Fri, Mar 28, 2014 at 11:31 AM, Myrna Walker <mwalke13 at iit.edu> wrote:

> Dear All,
>
>
>
> Please join the Xuan Zhou for his comprehensive exam.
>
>
>
> When: Wednesday, April 2, 2014, 10:00 am
>
> Where: Stuart Building - Room 223
>
>
> Title: TRACTABILITY OF FUNCTION APPROXIMATION PROBLEMS WITH GENERAL
> KERNELS
>
> Abstract: This talk addresses the problem of approximating functions
> belonging to a reproducing kernel Hilbert space. Often convergence rates
> deteriorate quickly as the dimension of problem increases. Such a behavior
> is known as the curse of dimensionality. Therefore it is desirable to have
> dimension independent convergence rates, which corresponds to the concept
> of strong polynomial tractability. Such tractability results have been
> established for anisotropic Gaussian reproducing kernels.
>
>
>
> We study the conditions for tractability on more general kernels of
> product form. The shape parameter, gamma, governs the horizontal scale of a
> function with respect to different input variables. We also introduce a
> parameter, alpha, which governs the vertical scale of the function with
> respect to different variables. The exponent of strong tractability depends
> on how quickly the sequence (alpha*gamma) tends to zero.
>


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