A DEVELOPMENT OF THE CRITERION METHOD FOR GENERALIZED DIAGONALLY DOMINANT MATRICES AND A STUDY OF THE ITERATIVE METHOD FOR PARALLEL PROCESSING

用迭代法对线性方程组Ax=B进行了数值计算。在这个项目中，我们提出了一个新的准则，并通过一些数值实验表明我们的准则比其他的准则简单。进一步对该方法的有效性进行了验证，结果表明该方法在求解线性方程组时是有效的。在1999年，我们改进了广义对角占优矩阵（G.D.D.M.）的迭代型判据。在2000年，我们将该准则应用于一些实际的算例，进一步证实了该方法的有效性。因此，我们尝试对一些II-矩阵建立了直接判别法，并成功地发展了比高一鸣等人的方法更少的方法。接下来我们的课题是对更多的H-矩阵进行数值实验，并证明其数学有效性。

The numerical computation is carried out to solve the linear systems Ax=b by using the iterative method. In this project we presented new criterion and showed that our criterion is simpler than other's with some numerical experiments. Further we tested the effectivity of the proposed method, and we obtained that our method is effective in solving the linear systems. Thus, we developed a simple method for judging II-matrix.In 1999th, we improved the iteration type as the criterion of the Generalized Diagonally Dominant Mtrix (G.D.D.M.). Then, We are adapted this method to some examples, and obtained better results.In 2000th, we are adapted this criterion to some practical examples , and furthermore we confirmed the availability of this method. So we became a ware of an own peculiarity of G.D.D.M.Therefore we test to develop the direct criterion for some II-matrices and succeeded in developping the method less than Yiming Gao, s.Coming our subject is testing some numerical experiment for much more H-matrices and to prove the mathematical validity.