Chebysheff-halley-like methods in banach spaces

Journal of Applied Mathematics and Computing

Volumn 4, Issue 1, 1997, Pages 83-107

  Argyros, Ioannis K ^a  

^a CAMERON UNIVERSITY   (United States)

Author keywords

Banach space; Chebysheff method; Hally method; Kantorovich hypotheses; Newton method

Indexed keywords

ANGULAR DISTRIBUTION; BANACH SPACES; INTEGRAL EQUATIONS; NEWTON-RAPHSON METHOD;

CHEBYSHEFF METHOD; COMPUTATIONAL COSTS; FRECHET DERIVATIVE; HALLEY-LIKE METHODS; HALLY METHOD; KANTOROVICH HYPOTHESES; NONLINEAR INTEGRAL EQUATIONS; SOLVING NONLINEAR EQUATIONS;

NONLINEAR EQUATIONS;

EID: 84875939314     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf03011382     Document Type: Article

References (14)

1. Argyros, I.K. Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc. 32, (1985), 275-292.
2. Argyros, I.K. On a class of nonlinear integral equations arising in neutron transport, Aequationes Mathematicae, 36, (1988), 99-111.
3. Argyros, I.K. On the convergence of an Euler-Chebysheff type method under Newton-Kantorovich hypotheses, Pure Mathematics and Applications, Vol. 4, No. 3, (1993), 369-373.
4. Argyros, I.K. A note on the Halley method in Banach spaces, Appl. Math. Comp. 58, (1993), 215-224.
5. Argyros, I.K. and Szidarovszky, F. The theory and applications of iteration methods, C.R.C. Press, Inc. Boca Raton, Florida, 1993.
6. Chandrasekhar, S. Radiative transfer, Dover Publ., New York, 1960.
7. Chen, D. On the convergence and optimal error estimates of King's iteration procedures for solving nonlinear equations, Intern. J. Computer Math. 26, (3 + 4), (1989), 229-237.
8. Chen, D. Kantorovich-Ostrowski convergence theorems and optimal error bounds for Jarratt's iterative methods, Intern. J. Computer Math. 31, (3 + 4), (1990), 221-235.
9. Mertvecova, M.A. An analog of the process of tangent hyperbolas for general functional equations (Russian), Dokl. Akad. Nauk SSSR, 88, (1953), 611-614.
10. Necepurenko, M.T. On Chebysheff's method for functional equations (Russian), Usephi Mat. Nauk. 9, (1954), 163-170.
11. Ortega, J.M. and Rheinboldt, W.C. Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970.
12. Ostrowski, A.M. Solution of equations in Euclidean and Banach spaces, Academic Press, New York, 1973.
13. Potra, F.A. On an iterative algorithm of order 1.839 for solving nonlinear operator equations, Numer. Funct. Anal. Optimiz. 7 (1), (1984-1985), 75-106.
14. Szidarovszky, F. and Palusinski, O. A special matrix equation and its applications in microelectronics, Appl. Math. Comp., 64, (1994), 115-119.