Results on the Chebyshev method in banach spaces
DOI:
https://doi.org/10.22199/S07160917.1993.0002.00002Keywords:
Numerical Solutions of Nonlinear operator equations, Banach spaces, Chebyshev iterative method, Kantorovich-type convergence, Newton-Kantorovich assumptions, Error bound expressionAbstract
In this paper, under standard Newton-Kantorovich conditions, we establish the Kantorovich-type convergence theorem for Chebyshev method in Banach spaces.References
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[2] Argyros, I.K.: On a class of nonlinear integral equations arising in Neutron Transport. Aequations Mathematicae, 36 (1988), 99-111.
[3] Chen, D.: Standard Kantorovich theorem of the Chebyshev method on complex plane. Intern. J. Computer Math., 42:(1+2) (1993), 67-70.
[4] Gragg, W.B.; Tapia, R.A.: Optimal error bounds for Newton-Kantorovich Theorem. SIAM J. Numer. Aual., 11 (1974), 10-13.
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[7] Rall, L.B.: Computational Solution of Nonlinear Operator Equations. John Wiley & sons, Inc., New York, 1969.
[8] Yamamoto, T.: On the methos of Tangent Hyperbolas in Banach Spaces. J. Computational and Applied Math., 21(1988), 75-88.
[2] Argyros, I.K.: On a class of nonlinear integral equations arising in Neutron Transport. Aequations Mathematicae, 36 (1988), 99-111.
[3] Chen, D.: Standard Kantorovich theorem of the Chebyshev method on complex plane. Intern. J. Computer Math., 42:(1+2) (1993), 67-70.
[4] Gragg, W.B.; Tapia, R.A.: Optimal error bounds for Newton-Kantorovich Theorem. SIAM J. Numer. Aual., 11 (1974), 10-13.
[5] Kantorovich, L.V.; Akilov, G.P.: Functional Analysis in Normed Spaces. Pergamon Press, New York, 1964.
[6] Ostrowski, A.M.: Solution of Equations in Euclidean and Banach Spaces. Academic Press, New York, 3rd ed., 1973.
[7] Rall, L.B.: Computational Solution of Nonlinear Operator Equations. John Wiley & sons, Inc., New York, 1969.
[8] Yamamoto, T.: On the methos of Tangent Hyperbolas in Banach Spaces. J. Computational and Applied Math., 21(1988), 75-88.
Published
2018-04-03
How to Cite
[1]
I. K. Argyros and D. Chen, “Results on the Chebyshev method in banach spaces”, Proyecciones (Antofagasta, On line), vol. 12, no. 2, pp. 119-128, Apr. 2018.
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