一类弱Lipschitz条件(m阶F-导数)下的Newton迭代  

CONVERGENCE OF NEWTON ITERATION UMDER WEAKER LIPSCHITZ CONDITION

作　　者：孔宪明[1] 胡中永[1] 房亮[1] 

机构地区：[1]泰山学院数学与系统科学系,山东泰安271021

出　　处：《山东农业大学学报（自然科学版）》2007年第3期477-480,483,共5页Journal of Shandong Agricultural University：Natural Science Edition

摘　　要：对算子F的m阶F-导数所满足的Lipschitz条件进行讨论,使得Newton法的应用范围得以扩展。在新的收敛条件A下,通过使用一种基于递归关系的技巧,证明了Newton法收敛,并给出了方程的解的存在唯一性定理。This paper, concernes with the weaker Lipschitz condition which is satisfied by the m - th Frechet - derivative of operator. A new Lipschitz - type condition is provided and a convergence theorem for Newton＇s method is given under this condition. This result is more convenient to apply. Hence, it has theoretic and practical value.

关 键 词：NEWTON迭代 LIPSCHITZ条件 收敛 

分 类 号：Q31[生物学—遗传学] S965.3[农业科学—水产养殖]