On convergence criteria for jarratt's method |
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Authors: | HA Chase |
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Institution: | Department of Mathematics, New Jersey Institute of Technology, 323 High Street, Newark, NJ 07102, USA U.S.A. |
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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. |
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