摘要
通过分析指出:Newton-Raphson法解一元非线性方程f(x)=0时发生振荡甚至发散的原因之一,是x_k(x_k是包括初值在内的估计值)与方程的根x~*之间,f(x)曲线与x轴之间有局部极近点即奇异点存在。基于上述分析,本文提出了一种搜索法以避开振荡区,从而加速收数、避免发散。并通过实例说明了本文方法在化工计算中的应用。
Through analysis, we pointed out that one of the reasons of oscillation or divergence while solving nonlinear equation of one un-known, f(x)=O, by Newton-Raphson method is that there exists a local-extreme-closed point between x_κ(x_κ is the estimated value of the root) and the root x~*, and the curve of f(x) and X-axis. Based on the analysis, a modified method is proposed in this paper. The main strategy is that while oscillating in itera-tion, searching procedure is taken in order to avoid the oscillation area and increase divergence. Examples show the application of the proposed method in chemical engineering calculations.
出处
《河北工学院学报》
1993年第2期14-19,共6页
Journal of Hubei Polytechnic University
关键词
非线性方程
奇异点
化工计算
Nonlinear equation
Newton-Raphson method
Singular point
Chemical engineering calculation
Solution of equations
