Convergence theorems for block splitting iterative methods for linear systems

In this paper, we will present the block splitting iterative methods with general weighting matrices for solving linear systems of algebraic equations Ax=b$\mathit{Ax}=b$ when the coefficient matrix A is symmetric positive definite of block form, and establish the convergence theories with respect to the general weighting matrices but special splittings. Finally, a numerical example shows the advantage of this method.