Multipoint super-halley type approximation algorithms in Banach spaces

Numerical Functional Analysis and Optimization

Volumn 21, Issue 7-8, 2000, Pages 845-858

  Ezquerro, J A ^a   Hernandez M A ^a  

^a UNIVERSITY OF LA RIOJA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; OPTIMIZATION; PROBLEM SOLVING; THEOREM PROVING;

BANACH SPACES; KANTOROVICH CONVERGENCE THEOREMS; MULTIPOINT ITERATION; MULTIPOINT SUPER HALLEY TYPE ALGORITHMS; NEWTON-KANTOROVICH ASSUMPTIONS; NONLINEAR OPERATOR EQUATION;

APPROXIMATION THEORY;

EID: 0343725794     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630560008816989     Document Type: Article

References (12)

1. V. Candela and A. Marquina, Recurrence Relations for Rational Cubic Methods I: The Halley Method, Computing 44 (1990) 169-184.
2. V. Candela and A. Marquina, Recurrence Relations for Rational Cubic Methods II: The Chebyshev Method, Computing 45 (1990) 355-367.
3. D. Chen, I. K. Argyros and Q. Qian, A Local Convergence Theorem for the Super-Halley Method in a Banach Space, Appl. Math. Lett. 7,5 (1994) 49-52.
4. B. Döring, Einige sätze über das Verfahren der tangierenden Hyperbeln in Banach-Räumen, Aplikace Mat. 15 (1975) 418-464.
5. J. M. Gutiérrez and M. A. Hernández, A Family of Chebdyshev-Halley Type Methods in Banach Spaces, Bull. Austral. Math. Soc. 55 (1997) 113-130.
6. M. A. Hernández, Newton-Raphson's Method and Convexity, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22, 1 (1992) 159-166.
7. L.V. Kantorovich, The Majorant Principle for Newton's Method, Dokl. Akad. Nauk SSSR 76 (1951) 17-20.
8. F. A. Potra and V.Pták, Nondiscrete Induction and Iterative Processes (Pitman, New York, 1984).
9. L. B. Rall, Quadratic Equations in Banach Spaces, Rend. Circ. Mat., Palermo (2), 10 (1961) 314-332.
10. R. A. Safiev, On some iterative processes, Ž. Vyčcisl. Mat. Fiz. 4 (1964) 139-143 Translated into English by L.B. Rall as MRC Technical Summary Report, No. 649, Univ. Wisconsin-Madison, 1966).
11. R. A. Safiev, On some iterative processes, Ž. Vyčcisl. Mat. Fiz. 4 (1964) 139-143 Translated into English by L.B. Rall as MRC Technical Summary Report, No. 649, Univ. Wisconsin-Madison, 1966).
12. T. Yamamoto, A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions, Numer. Math. 49 (1986) 203-220.