How to Cope with the Curse of Dimensionality?

Multivariate problems occur in many applications. They are defined on spaces of d-variate functions and d is often huge. Many multivariate problems suffer from the curse of dimensionality. This means that the minimal number of function values needed to compute an approximation to within ε is an exponential function of d.

In this talk we discuss how the curse of dimensionality can be vanquished by:

• switching to spaces with increasing smoothness of successive variables,
• switching to weighted spaces,
• switching to more lenient settings.

Event Topic:

Computational Mathematics & Statistics