CAJ | 학술논문

对牛顿迭代公式进行改进，构造了新的迭代公式，并证明了其在单根附近至少具有二阶收敛性；以按揭贷款问题为算例，在MATLAB7．1软件环境下编程，对简单迭代法、牛顿法、改进的算法进行了计算比较。结果表明，改进的算法不仅比简单迭代法收敛速度快、精度高，而且比牛顿法的精度高。
대우돈질대공식진행개진，구조료신적질대공식，병증명료기재단근부근지소구유이계수렴성；이안게대관문제위산례，재MATLAB7．1연건배경하편정，대간단질대법、우돈법、개진적산법진행료계산비교。결과표명，개진적산법불부비간단질대법수렴속도쾌、정도고，이차비우돈법적정도고。
The Newton iterative formula was improved ,and a new iterative formula was constructed. It proved that the new iterative formula had at least second order convergence rate at single root. Taking mortgage loans for ex- ample,simple iterative method,Newton iterative method and improved method were carried on comparison with calculation in the MATLAB 7.1. The results showed that improved method converged more quickly than simple iterative method,and the method was higher in precision than simple iterative method and Newton method.