On convergence criteria for jarratt's method |
| |
| Authors: | HA Chase |
| |
| Institution: | Department of Mathematics, New Jersey Institute of Technology, 323 High Street, Newark, NJ 07102, USA U.S.A. |
| |
| Abstract: | Let f(χ) together with its first two derivatives be continuous in the domain D and additionally let χM?D be an extremum (or turning point) of this function. Also, let χn+1 = T (χn,χn-1,χn-2) be Jarratt's Method for computing the extremum (or turning point) of a function. Criteria are demonstrated which insure that, for any triple of initial assumptions (χ1,χ0,χ-1)?D, Jarratt's Method, converges to the extremum of f(χ), and that from and after some n = N0, the rate of convergence of this method increases steadily, finally becoming unbounded when the solution χM is attained. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
