求解线性方程组的迭代法的统一二维迭代法
A UNIFIED APPROACH FOR SOL VING LINE AR EQUATIONSTWO-DIMENSIONAL ITERATIVE METHOD
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摘要: 求解线性方程组Ax=b的迭代法有其独特的实用意义,但由于其收敛的问题而受到限制。本文导出了常用的雅各比法、高斯-塞德尔法和逐次超松弛法等的统一方法,称之为二维迭代法,并由此得到了从新的角度改进迭代法的收敛性和收敛速度的途径。理论分析和数值计算都表明该方法优于常用的迭代法。此方法在解大规模电路中有用,例如用于VLSI的模拟。
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Abstract: In this paper, a unified approach of iterative methods, such as Jacobi method, Gauss-Seidel method, SOR method, etc., for solving linear equations is discussed and studied. For the reason stated in this paper, this approach is called 2-dimensional iterative method. The convergence and the rate of convergence of iteration process are improved by using this new approach. The theoretical analysis and the computing results demonstrate that this approach has many advantages over the generally used iterative methods. it is useful in solving the large scale electric circuits, such as VLSI. -
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