In this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds the preconditioned system. Several numerical examples are provided to demonstrate efficiency of preconditioner, especially stochastic problems large variance.

We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on the orthogonality among the block rows obtained by the partitioning method. The proposed method takes numerical orthogonality among block rows into account b...