Randomization for continuous problems

Maturity randomization for stochastic control problems

We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called Canadization procedure suggested by P. Carr in [2] for the fast computation of American put option prices. In addition to the original applicati...

Mendelian Randomization with a Continuous Outcome

Introduction This module computes the sample size and power of the causal effect in Mendelian randomization studies with a continuous outcome. This analysis is used in observational studies where clinical trials are not possible. Analogous to randomized clinical trials (RCT), Mendelian randomization (MR) divides subjects into two or more groups. However, MR uses a genetic variable, such as the ...

Subspace Iteration Randomization and Singular Value Problems

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any given fixed rank. However, the SVD is also known to be very costly to compute. Among the different approaches in the literature for computing low-rank approxima...

Linear, Semidefinite Programming and Randomization Methods for Combinatorial Optimization Problems

Quantum algorithms for continuous problems

Many problems in science and engineering are formulated using continuous mathematical models. Usually they can only be solved numerically and therefore approximately. Since they are often difficult to solve on a classical computer it’s interesting to investigate whether they can be solved faster on a quantum computer. After a brief introduction to quantum algorithms we report on a wide range of...