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 …

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 …

Three Monte Carlo methods for matrix inversion (MI) and finding a solution vector of a
system of linear algebraic equations (SLAE) are considered: with absorption, without …

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 …

In this paper, we introduce the “Walk on Equations”(WE) Monte Carlo algorithm, a novel
approach for solving linear algebraic systems. This algorithm shares similarities with the …

A new Monte Carlo estimator for solving the matrix equation x= Hx+ b is presented, and
theoretical results comparing this estimator with the traditional terminal and collision …

In this paper we present a stochastic SPAI pre-conditioner. In contrast to the standard
deterministic SPAI pre-conditioners that use the Frobenius norm, we present a Monte Carlo …

With the latest developments in the area of advanced computer architectures, we are
already seeing large scale machines at petascale level and we are faced with the exascale …