- 期刊
The Kinematics Design with the secant-homotopy Continuation Method
以正割連續法解運動設計學問題
摘要
本論文巧妙的結合正割法(secant theory)與連續法(homotopy continuation technique)，修改傳統牛頓法(Newton-Raphson method)成為新的正割連續法(secant-homotopy continuation method)，並且將之運用在運動設計學(kinematics design)問題上。利用本方法在求解非線性方程式(nonlinear equations)時，可藉由選擇適當的輔助函數(auxiliary function)而達到收斂(convergence)的效果，這是傳統牛頓法所不及之處，可大大降低牛頓法選擇起始值(initial values)試誤所浪費掉的時間及疊代(iteration)運算之後發散(divergence)的危險性。
關鍵字
無資料並列摘要
In this paper, the traditional Newton-Raphson method is modified by the secant theory and the homotopy continuation technique to a secant-homotopy continuation formula and is applied to the kinematics design problems. By means of choosing the auxiliary function, we can solve the nonlinear equations and guarantee the solutions exactly without divergence rather than the traditional numerical methods such as the Newton-Raphson method and so on.