This is the second volume of a three-volume set comprising a comprehensive study of the
tractability of multivariate problems. The second volume deals with algorithms using …

Tractability of multivariate problems has become a popular research subject. Polynomial
tractability means that the solution of a d-variate problem can be solved to within ε with …

We study the information complexity in the randomized setting of solving a general elliptic
PDE of order 2m in a smooth, bounded domain Q⊂ Rd with smooth coefficients and …

We study path integration on a quantum computer that performs quantum summation. We
assume that the measure of path integration is Gaussian, with the eigenvalues of its …

We present a survey of results on minimal errors and optimality of algorithms for strong and
weak approximation of systems of stochastic differential equations. For strong …

We study the minimal number n (ɛ, d) of information evaluations needed to compute a worst
case ɛ-approximation of a linear multivariate problem. This problem is defined over a …

In recent work of Hairer, Hutzenthaler and Jentzen,, a stochastic differential equation (SDE)
with infinitely differentiable andbounded coefficients was constructed such that the Monte …

We study the problem of approximating the distribution of the solution of a d-dimensional
system of stochastic differential equations (SDEs) at a single time point by a probability …

Many papers study polynomial tractability for multivariate problems. Let n (ɛ, d) be the
minimal number of information evaluations needed to reduce the initial error by a factor of ɛ …

Most continuous mathematical formulations arising in science and engineering can only be
solved numerically and therefore approximately. We shall always assume that we're dealing …