求解非线性方程的两个区间套算法  

TWO INTERVAL ENCLOSING ALGORITHMSFOR SOLVING NON-LINEAR EQUATION

作　　者：李阿然[1] 曹德欣[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《青岛大学学报（自然科学版）》2003年第4期1-7,共7页Journal of Qingdao University(Natural Science Edition)

基　　金：国家自然科学基金资助课题(50174051)。

摘　　要：利用Lagrange插值和Hermite插值对Alefeld,Potra的3种算法作了改进,构造了求解非线性方程f(x)=0在区间[a,b]中单根x 的两个区间套算法。与Alefeld,Potra的3种算法相比,这两个新算法的Q收敛阶和效率指数更高。证明了算法的收敛性,给出了收敛阶和效率指数。数值实验验证了算法是可靠和有效的。With the ideas of Lagrange interpolation and Hermit interpolation,two interval enclosing algorithms for solving the single root of nonlinear equation f(x)=0 are presented. The Q -convergence order and efficiency index of these two algorithms are higher than those in Alefeld and Potra's. The convergence is proved. Numerical results also show that the algorithms are reliable and efficient.

关 键 词：非线性方程 区间套算法 收敛阶 效率指数 插值函数 LAGRANGE插值 HERMITE插值 收敛性 

分 类 号：O241.7[理学—计算数学]