在解非線性方程組的領域中牛頓 - 拉弗森一直被多數人所採用，本研究的目的是探討牛頓型疊迭代法加入二次項的效果。一般而言，計算二次項雖然對於高次項方程式以及較遠的初始值會有較牛頓法佳的收斂表現，但仍無法確實掌握其行為，本研究即針對此進行了深入的討論。更混合了加入二次項的方法與牛頓法來進行迭代計算。 本研究是把加入二次項的早差分法、混合法與牛頓法作比較。針對不同的方程式進行迭代，探討以下項目 : (1) 迭代次數。 (2) 平均每次迭代計算的CPU時間。 (3) 不同類型的方程式對於迭代時間和迭代次數的影響。 When solving nonlinear equations the Newton - Raphson method is used by many people. This research studies a Newton-type method which takes the second order terms into account. It was believed that the precise mechanism is still not well understood. This project compares the method having the second order terms with the Newton — Raphson’s method. For problems with different nonlinear equations the following items are investigated: (1)Numbers of iterations in the computations. (2)The influence of different kind of equations to number of iteration and CPU time.
