The Monte Carlo method is inherently parallel and the extensive and rapid development in
parallel computers, computational clusters and grids has resulted in renewed and …

A new Walk on Equations (WE) Monte Carlo algorithm for solving systems of linear algebraic
(LA) equations is proposed and studied. This algorithm relies on a non-discounted sum of …

The question “what Monte Carlo models can do and cannot do efficiently” is discussed for
some functional spaces that define the regularity of the input data. Data classes important for …

We consider hybrid deterministic‐stochastic iterative algorithms for the solution of large,
sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we …

Abstract Methods based on Monte Carlo for solving linear systems have some interesting
properties which make them, in many instances, preferable to classic methods. Namely …

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 …

In this paper we analyse applicability and robustness of Markov chain Monte Carlo
algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices …

The results of a parallel implementation of a randomized vector algorithm for solving
systems of linear equations are presented in the paper. The solution is represented in the …

We propose a novel stochastic algorithm that randomly samples entire rows and columns of
the matrix as a way to approximate an arbitrary matrix function using the power series …

Abstract Quasi-Monte Carlo methods are based on the idea that random Monte Carlo
techniques can often be improved by replacing the underlying source of random numbers …