论文部分内容阅读
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。
The iterative method of solving linear equations Ax = b has its unique practical significance, but it is limited because of its convergence problem. This paper derives the common methods of Jacobian, Gauss-Seidel and successive over relaxation methods, which are called two-dimensional iterative method, and thus obtain the convergence and convergence speed of the iterative method from a new perspective Way. Both theoretical analysis and numerical calculation show that this method is superior to the commonly used iterative method. This method is useful in solving large-scale circuits, for example for VLSI simulation.