Multi Index Method
Multi index methods are based on Sparse Grid methods and utilize the extra mixed regularity between dimensions (spatial or stochastic) to reduce the work complexity of different methods. In fact, in some cases we may get the rate of work complexity that is independent of the number of dimensions.
Overview
Details
Multi index methods are based on Sparse Grid methods and utilize the extra mixed regularity between dimensions (spatial or stochastic) to reduce the work complexity of different methods. In fact, in some cases we may get the rate of work complexity that is independent of the number of dimensions. We have developed a Mutli Index variant of the Monte Carlo (MIMC) method and we are currently developing a Multi Index variant of the Stochastic Collocation (MISC) method.
Collaborators
- Abdul Lateef Haji Ali (KAUST)
- Fabio Nobile (EPFL)
- Lorenzo Tamellini (EPFL)
- Raul Tempone (KAUST)
Publications
- Abdul-Lateef Haji-Ali, Fabio Nobile, Raul Tempone, Multi-Index Monte Carlo: When Sparsity Meets Sampling, Numerische Mathematik, pp 1-40, June 2015.
