Homeier, Herbert H. H. (2005) On Newton-type methods with cubic convergence. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 176 (2). pp. 425-432. ISSN 0377-0427,
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Recently, there has been some progress on Newton-type methods with cubic convergence that do not require the computation of second derivatives. Weerakoon and Fernando (Appl. Math. Lett. 13 (2000) 87) derived the Newton method and a cubically convergent variant by rectangular and trapezoidal approximations to Newton's theorem, while Frontini and Sormani (J. Comput. Appl. Math. 156 (2003) 345; 140 (2003) 419 derived further cubically convergent variants by using different approximations to Newton's theorem. Homeier Q. Comput. Appl. Math. 157 (2003) 227; 169 (2004) 161) independently derived one of the latter variants and extended it to the multivariate case. Here, we show that one can modify the Werrakoon-Fernando approach by using Newton's theorem for the inverse function and derive a new class of cubically convergent Newton-type methods. (C) 2004 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | 3RD-ORDER CONVERGENCE; VARIANT; rootfinding; Newton method; Newton-type method; Newton theorem; inverse function; iterative methods; nonlinear equations |
| Subjects: | 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 May 2021 05:19 |
| Last Modified: | 17 May 2021 05:19 |
| URI: | https://pred.uni-regensburg.de/id/eprint/36255 |
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