论文信息 - OnQ-order andR-order of convergence

OnQ-order andR-order of convergence

We give sufficient conditions for a sequence to have theQ-order and/or theR-order of convergence greater than one. If an additional condition is satisfied, then the sequence has an exactQ-order of convergence. We show that our results are sharp and we compare them with older results.

F. Potra

[1] D. D. Wall. The order of an iteration formula , 1956 .

[2] D. D. Wall. Note on Predictor-Corrector Formulas , 1956 .

[3] J. E. Dennis,et al. On Newton-like methods , 1968 .

[4] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[5] R. Brent. Some Efficient Algorithms for Solving Systems of Nonlinear Equations , 1973 .

[6] A. Ostrowski. Solution of equations in Euclidean and Banach spaces , 1973 .

[7] Joseph F. Traub,et al. Asymptotic behavior of vector recurrences with applications , 1977 .

[8] Comparaison de Suites Convergentes , 1977 .

[9] H. Schwetlick. Numerische Lösung nichtlinearer Gleichungen , 1978 .

[10] W. Rheinboldt. Schwetlick H., Numerische Lösung nichtlinearer Gleichungen. Berlin VEB Deutscher Verlag der Wissenschaften 1979. 346 S., 21 Abb., M 68,— , 1980 .

[11] F. Potra,et al. Nondiscrete induction and iterative processes , 1984 .