Related papers: A Monte Carlo algorithm for efficient large matrix…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient…
Monte Carlo rendering algorithms are widely used to produce photorealistic computer graphics images. However, these algorithms need to sample a substantial amount of rays per pixel to enable proper global illumination and thus require an…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Convergence of the method is proved and its convergence rate studied. Results in high dimension for different kind of non-linearities show…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
Discontinuous visibility changes remain a major bottleneck when optimizing surfaces within a physically-based inverse renderer. Many previous works have proposed sophisticated algorithms and data structures to sample visibility silhouettes…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
New machine learning based algorithms have been developed and tested for Monte Carlo integration based on generative Boosted Decision Trees and Deep Neural Networks. Both of these algorithms exhibit substantial improvements compared to…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The…
While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…
We present a new Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix. It extends the power method and uses a new sampling method, the sewing method, that does a large state…