SCHWARZ ALTERNATING PROCEDURE WITH RELAXATION FACTOR
带松弛因子的Schwarz交替方法

The Schwarz alternating procedure(SAP) for solving two-point boundary value problem is considered. Two algorithms for solving the problem are given when the interval0,1] is di-vided into two subintervals or m subintervals, respectively. In some sense, the algorithms are direct methods. Another SAP with relaxation factor for solving two-dimensional problems is discussed, and its optimal relaxation factor Wopt is given. For the factor Wopt the error estimates are established. It is also proven that the SAP with Wopt is better than the scheme discussed in3] with its optimal factor. All methods presented can be used to solve relevant discrete problems.