Convergence analysis for the Secant method based on new recurrence relations  

作　　者：BI Wei-hong REN Hong-min WU Qing-biao 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China [2]College of Information and Engineering, Hangzhou Radio and TV University, Hangzhou 310012,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2008年第4期447-454,共8页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China (10871178);the Natural Science Foundation of Zhejiang Province of China (Y606154);Foundation of the Education Department of Zhejiang Province of China (20071362)

摘　　要：A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.

关 键 词：Secant method Banach space recurrence relation semilocal convergence Lipschitz continuous divided difference 

分 类 号：O17[理学—数学]