不精确Newton法与Broyden法的仿射不变收敛性  

ON THE AFFINE INVARIANT CONVERGENCE THEOREMS OF INEXACT NEWTON METHOD AND BROYDEN’S METHOD

作　　者：白中治[1] 童培莉[1] 

机构地区：[1]复旦大学数学所,上海科技大学计算机科学系

出　　处：《电子科技大学学报》1994年第5期535-540,共6页Journal of University of Electronic Science and Technology of China

摘　　要：给出了不精确Ｎｅｗｔｏｎ法的半局部收敛性定理，通过改善条件γ＿ｋ／Ｆ（ｘ￣ｋ）≤η＿ｋ（ｋ＝０，１…）使其具仿射不变性，建立起了不精确Ｎｅｗｔｏｎ法的具仿射不变性的半局部收敛定理，在一定条件下，讨论了Ｂｒｏｙｄｅｎ方法的具仿射不变性的存在──收敛定理，从而，扩大了这两种方法收敛定理的收敛域。this paper gives a semilocal convergence theorem for the inexact Newton meth-od and sets up its affine invariant semilocal convergence theorem by improving the conditionto have the affince invariant property. Under certain condi-tions,the existence convergence theorem of Broyden’s method which is affine invariant is dis-cussed.The convergence regions of the cowergenee theorems of these two methods areexpanded.

关 键 词：不精确牛顿法 Broyden法 仿射不变性 收敛性 

分 类 号：O241.5[理学—计算数学]