Probabilistic-algebraic algorithms of Monte Carlo methods
Ilia N. Medvedev, Guennady A. Mikhailov · Russian Journal of Numerical Analysis and Mathematical Modelling · 2011
The theory of scalar and vector probabilistic–algebraic algorithms of the Monte Carlo method used in the solution of systems of integral equations is detailed and refined in the paper. A dual representation of the mean square of a vector estimate is constructed. Scalar algorithms are formulated, and a comparison of vector and scalar estimates of the solution is given for the first time. A criterion of finiteness of vector estimate variance is constructed on this basis.