A computational method for large-scale differential symmetric Stein equation

We propose a numerical method for solving large-scale differential symmetric Stein equations having low-rank right constant term. Our approach is based on projection the given problem onto a Krylov subspace then solving the low dimensional matrix problem by using an integration method, and the original problem solution is built by using obtained low-rank approximate solution. Using the extended block Arnoldi process and backward differentiation formula (BDF), we give statements of the approximate solution and corresponding residual. Some numerical results are given to show the efficiency of the proposed method.