由於牛頓-拉弗森的收斂性太依賴於初始值，實際上，非線性方程式較複雜時，選取保證收斂的初始值是困難的。本研究的目的是在於嘗試發展新的方法，使在求解非線性方程式時，不需考慮初始值的位置，也就是發展一種宏觀收斂(Globally Convergent)的方法，加以改良牛頓-拉弗森來求解非線性方程式。
本研究將新發展出的座標平移法與其他宏觀收斂的迭代法做運算速度上的比較，以期對工程應用中求解非線性方程式能有所幫助。

When solving nonlinear equations the Newton-Raphson method is used by many people . But when we use the Newton-Raphson method to solve nonlinear equations , we must give the initial value close to the solution . This research studies a new method which is globally convergent. The new method improves the Newton-Raphson method . Then we can solve nonlinear equations by giving the initial value which is not close to the solution. We also compare the velocity of the new method with other globally convergent methods .

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