求解方程近似解的改进双曲线型迭代算法

Modified hyperbola iterative algorithm for approximately solving equation

应用双曲线逼近法 ,在分析了迭代算法思想的基础上 ,结合过程模拟与系统仿真的实际 ,推导出求解方程f(x) =0近似根新型迭代算法 ,并给出了迭代格式和计算方法。计算结果表明 ,用此算法求解方程的根 ,收敛速度及稳定性均好于割线法 ,初值选取范围比牛顿法和割线法宽。

A new iterative algorithm is proposed by using the hyperbola approach method, analyzing the fundamentals of iterative algorithm and considering the process simulation simultaneously. The iterative format and the iterative calculating ruler of the new algorithm are given. The simulated results show that the convergence speed is faster than that of Secant iterative algorithm and the convergence stability is better than that of Secant iterative algorithm and Newton iterative algorithm. Moreover, the selective range of the value is also widened. Thus the proposed new iterative algorithm is significant in solving equations both theoretically and practically.