A new type of recurrence relations for the secant method

International Journal of Computer Mathematics

Volumn 72, Issue 4, 1999, Pages 477-490

  Hernandez M A ^a   Rubio, M J ^a  

^a UNIVERSITY OF LA RIOJA   (Spain)

Author keywords

A priori error bounds; Recurrence relations; The Secant method

Indexed keywords

BANACH SPACES; BOUNDARY VALUE PROBLEMS; ERROR ANALYSIS; ERRORS; MATHEMATICAL OPERATORS;

CONVERGENCE THEOREM; NONLINEAR BOUNDARY VALUE PROBLEMS; NONLINEAR OPERATOR EQUATIONS; NUMERICAL RESOLUTION; PRIORI ERROR BOUNDS; RECURRENCE RELATIONS; SECANT METHODS; SECOND ORDERS;

NONLINEAR EQUATIONS;

EID: 0012605421     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169908804870     Document Type: Article

References (15)

1. Argyros, I. K. (1993). On the Secant Method, Publ. Math. Debrecen, 43, 223-238.
2. Balazs, M. and Goldner, G. (1973). On Existence of Divided Differences in Linear Spaces, Rev. Anal. Numer. Theorie Approximation, 2, 3-6.
3. Dennis, J. E. (1969). On the Kantorovich Hypothesis for Newton's Method, SIAM J. Numer. Anal., 6, 493-507.
4. Gutierrez, J. M. and Hernandez, M. A. (1997). New Recurrence Relations for Chebyshev Method, Appl. Math. Lett., 10, 63-65.
5. Hernández, M. A. and Salanova, M. A., Chebyshev Method and Convexity, To appear in Appl. Math. Comput.
6. Moret, I. (1984). A Note on Newton Type Iterative Methods, Computing, 33, 65-73.
7. Potra, F. A. (1979). On a Modified Secant Method, Anal. Numer. Theor. Approx., 8, 203-214.
8. Potra, F. A. and Pták, V. (1984). Nondiscrete Induction and Iterative Processes (Pitman, New York).
9. Rheinboldt, W. C. (1968). A Unified Convergence Theory for a Class of Iterative Processes, SIAM J. Numer. Anal., 5(1), 371-391.
10. Rokne, J. (1972). Newton's Method under Mild Differentiability Conditions with Error Analysis, Numer. Math., 18, 401-412.
11. Schmidt, J. W. (1974). Regula-Falsi Verfahren mit Konsistenter Steigung und Majoranten Prinzip, Periodica Mathematica Hungarica, 5, 187-193.
12. Schröder, J. (1956). Nichtlineare Majoranten beim Verfahren der Schrittweissen Näherung, Arch. Math. (Basel), 7, 471-484.
13. Sergeev, A. (1961). On the Method of Chords, Sibirsk. Mat. Ž., 2, 282-289.
14. Ulm, S. (1967). Ob obobscennych Razdelenych Raznostjach, I, II, Eesti NSV Tead. Akad. Toimtised Füüs. Mat., 16, 146-156.
15. Ypma, T. J. (1984). Convergence of Newton-like Iterative Methods, Numer. Math., 45, 251-421.