Hermite算法的收敛性分析及其改进

Hermite method convergence analyses and improvement

为了提高多点切触加工算法的计算效率,对其中的Hermite算法进行了改进,并且对改进后的Hermite算法的收敛性进行了理论分析,推导了改进后算法的局部收敛条件,同时给出算法的Steffensen加速迭代公式并新提出了一种基于试算的待定系数迭代法.分析和实例表明,改进后的Hermite算法属于线性收敛的算法,而待定系数迭代法则有接近二阶的收敛速度.综合应用上述算法,可以满足一般性自由曲面多点切触加工刀位计算的要求.

To make multi-points tangent contact machining have higher computational efficiency, an improved algorithm based on Hermite method was proposed. Theoretical analyses were given on the convergence of the improved algorithm, and the constraints for local convergence of the new algorithm were also derived. Then the formula of steffensen accelerated iterative method was applied on the algorithm. Another novel algorithm called iterative method of undetermined coefficient based on trial method was developed. The results show that the improved algorithm based on Hermite method acts as a linear convergence method, while the iterative method of undetermined coefficient algorithm has the same convergence speed with square convergence method approximately. Then it can meet the demand for the tool path generating computation of general sculpture surface by combining all the above-mentioned algorithms applied on them.