Results on the Chebyshev method in banach spaces

  • Ioannis K. Argyros Cameron University.
  • Dong Chen University of Arkansas.
Palabras clave: Numerical Solutions of Nonlinear operator equations, Banach spaces, Chebyshev iterative method, Kantorovich-type convergence, Newton-Kantorovich assumptions, Error bound expression

Resumen

In this paper, under standard Newton-Kantorovich conditions, we establish the Kantorovich-type convergence theorem for Chebyshev method in Banach spaces.

Biografía del autor

Ioannis K. Argyros, Cameron University.
Department of Mathematics.
Dong Chen, University of Arkansas.
Department of Mathematical Sciences.

Citas

[1] Argyros, I.K.: Quadratic equations and applications to Chandrasekhar's and related equations. Bull. Austral. Math. Soc., 32 (1988), 275-292.

[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.
Publicado
2018-04-03
Cómo citar
Argyros, I., & Chen, D. (2018). Results on the Chebyshev method in banach spaces. Proyecciones. Journal of Mathematics, 12(2), 119-128. https://doi.org/10.22199/S07160917.1993.0002.00002
Sección
Artículos