Computational Mathematics and Statistics Seminar by Onyekachi (Osisiogu) Emenike: Generalized Tractability for Approximation Problems Defined on Hilbert Spaces

Speaker: Onyekachi (Osisiogu) Emenike

Title: Generalized Tractability for Approximation Problems Defined on Hilbert Spaces

Abstract:

The information complexity of a problem is the number of function data required to solve the problem within the desired error tolerance. A problem is tractable if the information complexity does not grow too large as the dimension of the problem increases or the error threshold decreases. Therefore, the purpose of tractability is to study the complexity with respect to d and ε^(−1). There are a number of tractability results for numerical problems, beginning in the 1990s (see [1]). In this talk we focus on unifying and generalizing many existing tractability results for approximation problems where all linear functional data is available. These generalizations provide equivalent conditions for (strong) tractability in terms of sums of functions of the singular values of the solution operators.

This is a joint work with Fred J. Hickernell and Peter Kritzer.

[1] H. Wozniakowski. Tractability and strong tractability of linear multivariate problems. J. Complexity, 10(1994), 96–128.

 

Computational Mathematics and Statistics Seminar

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