Local convergence analysis of two iterative methods
Tóm tắt
Từ khóa
Tài liệu tham khảo
Amat, S., M.A. Hernandez, and N. Romero. 2008. A modified Chebyshev’s iterative method with at least sixth order of convergence. Applied Mathematics and Computation 206: 164–174.
Argyros, I.K., and S. George. 2020. Mathematical modeling for the solution of equations and systems of equations with applications, vol. IV. New York: Nova Publishes.
Argyros, I.K., S. George, and A.A. Magreñán. 2015. Local convergence for multi-point-parametric Chebyshev–Halley-type methods of higher convergence order. Journal of Computational and Applied Mathematics 282: 215–224.
Argyros, I.K., and A.A. Magreñán. 2017. Iterative methods and their dynamics with applications. New York: CRC Press.
Argyros, I.K., and A.A. Magreñán. 2015. A study on the local convergence and the dynamics of Chebyshev–Halley-type methods free from second derivative. Numerical Algorithms 71: 1–23.
Chen, L., C. Gu, and Y. Ma. 2011. Semilocal convergence for a fifth order Newton’s method using recurrence relations in Banach spaces. Journal of Applied Mathematics 2011: 1–15.
Chun, C., P. Stanica, and B. Neta. 2011. Third-order family of methods in Banach spaces. Computers and Mathematics with Applications 61: 1665–1675.
Cordero, A., J.L. Hueso, E. Martinez, and J.R. Torregrosa. 2012. Increasing the convergence order of an iterative method for nonlinear systems. Applied Mathematics Letters 25: 2369–2374.
Cordero, A., M.A. Hernandez-Veron, N. Romero, and J.R. Torregrosa. 2015. Semilocal convergence by using recurrence relations for a fifth-order method in Banach spaces. Journal of Computational and Applied Mathematics 273: 205–213.
Ezquerro, J.A., and M.A. Hernandez-Veron. 2015. On the domain of starting points of Newton’s method under center Lipschitz conditions. Mediterranean Journal of Mathematics. https://doi.org/10.1007/s00009-015-0596-1.
Hueso, J.L., and E. Martinez. 2014. Semilocal convergence of a family of iterative methods in Banach spaces. Numerical Algorithms 67: 365–384.
Jaiswal, J.P. 2015. Semilocal convergence of an eighth-order method in Banach spaces and its computational efficiency. Numerical Algorithms 71: 933–951.
Ostrowski, A.M. 1977. Solution of equations in Euclidean and Banach spaces, 3rd ed. New York: Academic Press.
Proinov, P.D., and S.I. Ivanov. 2015. On the convergence of Halley’s method for multiple polynomial zeros. Mediterranean Journal of Mathematics 12: 555–572.
Parida, P.K., and D.K. Gupta. 2007. Recurrence relations for a Newton-like method in Banach spaces. Journal of Computational and Applied Mathematics 206: 873–887.
Traub, J.F. 1964. Iterative methods for the solution of equations. Englewood Cliffs: Prentice-Hall.
Zheng, L., and C. Gu. 2012. Recurrence relations for semilocal convergence of a fifth order method in Banach spaces. Numerical Algorithms 59: 623–638.
Ortega, J.M., and W.C. Rheinboldt. 1970. Iterative solution of nonlinear equations in general variables. New York: Academic Press.
Argyros, I.K., and S. George. 2018. Semilocal convergence analysis of a fifth-order method using recurrence relations in Banach space under weak conditions. Applied Mathematics 45 (2): 223–231.
Singh, S., D.K. Gupta, E. Martinez, and J.L. Hueso. 2016. Semilocal convergence analysis of an iteration of order five using recurrence relations in Banach spaces. Mediterranean Journal of Mathematics 13: 4219–4235.
George, S., I.K. Argyros, P. Jidesh, M. Mahapatra, and M. Saeed. 2021. Convergence analysis of a fifth order iterative method using recurrence relations and conditions on the first derivative. Mediterranean Journal of Mathematics 18: 57. https://doi.org/10.1007/s00009-021-01697-6.
Ostrowski, A.M. 1966. Solution of equations and systems of equations, vol. 9, 2nd ed. Pure and applied mathematics. New York: Academic Press.