A randomised iterative method for solving factorised linear systems

Abstract

For solving a linear system with a large-scale coefficient matrix which is stored in a factorised form, we present a new interlaced randomised iterative method. The new method can take advantage of the factored form and avoid performing matrix multiplications. Furthermore, its convergence property is studied and theoretical analysis reveals that it is linearly convergent. Finally, some numerical results are given to confirm the effectiveness of the proposed method.