CMX Lunch Seminar

Adaptive numerical algorithms expend computational effort necessary to meet the error tolerance requirements of the user. Besides constructing approximate solutions, adaptive algorithms also use function data to determine the computational effort required to obtain a satisfactory solution and how best to allocate that computational effort. The challenge is knowing what can be reliably learned from function data.

We contend that successful adaptive algorithms should be constructed for non-convex cones of input functions. We illustrate via some simple one-dimensional problems. Subsequently, we survey our work constructing adaptive (quasi-)Monte Carlo algorithms. Finally, we propose some research directions for adaptive algorithms based on cones of inputs.