Information-based complexity
On approximate recovery of functions with bounded mixed derivative
Journal of Complexity - Festschrift for Joseph F. Traub, Part 1
Explicit cost bounds of algorithms for multivariate tensor product problems
Journal of Complexity
A new algorithm and worst case complexity for Feynman-Kac path integration
Journal of Computational Physics
Worst case complexity of weighted approximation and integration over Rd
Journal of Complexity
Applicability of Smolyak's algorithms to certain banach spaces of multivariate functions
Journal of Complexity
Finite-order weights imply tractability of linear multivariate problems
Journal of Approximation Theory
The randomized information complexity of elliptic PDE
Journal of Complexity
On the complexity of parabolic initial-value problems with variable drift
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Generalized tractability for multivariate problems Part I
Journal of Complexity
Finite-order weights imply tractability of linear multivariate problems
Journal of Approximation Theory
On the complexity of parabolic initial-value problems with variable drift
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
The randomized information complexity of elliptic PDE
Journal of Complexity
Hi-index | 0.00 |
We study the multivariate Feynman-Kac path integration problem. This problem was studied in Plaskota et al. (J. Comp. Phys. 164 (2000) 335) for the univariate case. We describe an algorithm based on uniform approximation, instead of the L2-approximation used in Plaskota et al. (2000). Similarly to Plaskota et al. (2000), our algorithm requires extensive precomputing. We also present bounds on the complexity of our problem. The lower bound is provided by the complexity of a certain integration problem, and the upper bound by the complexity of the uniform approximation problem. The algorithm presented in this paper is almost optimal for the classes of functions for which uniform approximation and integration have roughly the same complexities.