Combining randomized and deterministic iterative algorithms for high accuracy solution of large linear systems and boundary integral equations

Abstract This article continues the research on combined stochastic-deterministic iterative algorithms for solving large system of linear algebraic equations we developed in our previous study [K. K. Sabelfeld and G. Agarkov, Randomized vector algorithm with iterative refinement for solving boundary integral equations, Monte Carlo Methods Appl. 30 2024, 4, 375–388]. In this paper we focus on two issues: Variance reduction and extension of randomized algorithms by combining them with Krylov type iterative methods like the method of conjugate gradients, the conjugate residual method, and Craig’s method. The developed randomized algorithms are applied to boundary integral equations for 2D and 3D Laplace equations.