This idea motivates us to propose the modified ASOR (MASOR) method for solving the saddle point problem (1) by making another splitting for the coefficient matrix of the saddle point problem (1) as follows:
where [M.sub.[alpha],[omega],[tau]] is the iteration matrix of the MASOR method and its form as follows:
Then, the algorithmic description of the MASOR method is as follows.
Note that the MASOR method involves three parameters [alpha], [omega], and [beta].
Note that the MASOR method with [beta] = 1/2 reduces to the ASOR method proposed by Njeru and Guo .
Then, the MASOR method is convergent for all [alpha], [omega], and [tau] such that
Semiconvergence of the MASOR Method for Singular Saddle Point Problem.
Together with Definition 6 and Lemmas 17 and 18, we get the following sufficient conditions for the semiconvergence of the MASOR method.
Then, the MASOR method is semiconvergentfor all [alpha], [beta], and [omega] such that
The Optimal Convergence Factors of the GASOR and MASOR Methods
According to the theory of iterative methods, the optimal parameters of the GASOR method and MASOR method are as follows:
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