A multi-scale Monte Carlo method for electrolytes

A Quasi Monte Carlo Method for Large-Scale Inverse Problems

We consider large-scale linear inverse problems with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we implement importance sampling schemes, specially tailored to the structure of inverse problems. We empha...

Multi-way Monte Carlo Method for Linear Systems

We study the Monte Carlo method for solving a linear system of the form x = Hx + b. A sufficient condition for the method to work is ‖H‖ < 1, which greatly limits the usability of this method. We improve this condition by proposing a new multi-way Markov random walk, which is a generalization of the standard Markov random walk. Under our new framework we prove that the necessary and sufficient ...

Slice Samoling as a Markov Chain Monte Carlo Method

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The Monte-Carlo Method

The Monte Carlo Method

The Monte Carlo method is often referred to as a ‘computer experiment’. One might think of this as a way of conveying the fact that the output of simulations is not an equation, as in conventional theory. Instead, numbers appear on the computer screen in somewhat the same way that numbers appear on a measuring device in the laboratory. Thus there is the implication that somehow simulations are ...