Algorithms of the block multisplitting and preconditioned Krylov iterative Method for linear systems of the form Ax=f are proposed,where A is block tridiagonal matrix. The convergence of these iterative methods is analysed,when A is an M matrix or H matrix.The resulting MPPE method and preconditioned AKrylov method have been tested on a Challenge L computer.Numerical examples indicates that the new method is very efficient,since the parallel computation can be applied.

In this paper, a method of approximation of ‖A^-1‖∞ is proposed. Some numerical examples are given

The algorithms of Vectorizable PE Method for linear systems of the form Ax=f are proposed, when A is block tridiagonal matrix. The convergence of these iterative methods is analysed, when A is an M matrix or H matrix. The resulting VPE method has been tested on YH-1 computer. Numericla examples indicate that the new method is very efficient, since the vectorial computation can be applied.

A modified two-parameter parallel Jacobi-Type algorithm (M2PPJ) for solving system of linear algebraic equations is proposed. The convergence and the optimum parametes of the method are analysed. The rate of convergence is more than two times as large as that of 2PPJmethod and the extrapolation method of J^2P. Numerical examples are given to illustrate these results which indicate the superiority of the present method.

The higher ordar parallel Jacobi-Type method for solving system of linear algebraic equations is proposed, the convergence of the method is analysed and the optimum parameters and the corresponding spectral radius of the iterative matrix for the model proplem and the like are given. In the end there are some numerical examples to illustrate the effectiveness of our method.

The convergence of BAORJ algorithm is considered and the optimum paramenters and the corresponding rate of convergence for the model problem are obtained. These results will benefit the use of BAORJ algorithm.

A simpler and more concrete estimate of the upper bound of ‖A^-1‖_∞ than those in previous papers is given, when A is an H-matrix and the equidiagonal dominant matrix is defined.We prove that if A is an equidiagonal-dominant M-matrix with equidiagonal-dominanceδ|i.e.|a₁₁-||a₁₁|=δ,∀_i),则ρ(A^-1)=‖A^-1‖_x=(A^-1)_ij=1/δ,∀_i, By use of equidiagonal-dominant matrix the upper bound of ‖A^-1‖_x for any H-matrx may be found. Several interesting examples are given to illustrate our theorems.