Block incomplete factorization preconditioners for a symmetric block-tridiagonal M-matrix

We propose new block incomplete factorization preconditioners for a symmetric block-tridiagonal M-matrix which can be computed in parallel, and then theoretical properties for these block preconditioners are studied. Spectral properties of the transformed coefficient matrices with the block incomplete factorization preconditioners are also examined to see the convergence rate of the preconditioned CG(PCG) method. Lastly, numerical results of the PCG using the block incomplete factorization preconditioners are compared with those of the PCG using a standard incomplete factorization preconditioner to see how effective the block incomplete factorization preconditioners are.