We study optimal quadrature formulas for convex functions in several variables. In particular, we answer the following two questions: Are adaptive methods better than nonadaptive ones? And: Are randomized (or Monte Carlo) methods better than deterministic methods?
We study the intrinsic difficulty of solving linear parabolic initial value problems numerically at a single point. We present a worst case analysis for determin-istic as well as for randomized (or Monte Carlo) algorithms, assuming that the drift coefficients and the potential vary in given function spaces. We use fundamental solutions (parametrix method)… (More)