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On iterative methods with accelerated convergence for solving systems of nonlinear equations. (English) Zbl 1226.90103

Summary: We present a modified method for solving nonlinear systems of equations with order of convergence higher than other competitive methods. We generalize also the efficiency index used in the one-dimensional case to several variables. Finally, we show some numerical examples, where the theoretical results obtained in this paper are applied.

MSC:

90C30 Nonlinear programming

Software:

MPFR
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References:

[1] Ostrowski, A.M.: Solutions of Equations in Euclidean and Banach Spaces. Academic Press, New York (1973) · Zbl 0304.65002
[2] Argyros, I.K., Chen, D., Qian, Q.: A local convergence theorem for the super-Halley method in a Banach space. Appl. Math. Lett. 7(5), 49–52 (1994) · Zbl 0811.65043
[3] Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs (1964) · Zbl 0121.11204
[4] Grau, M., Díaz-Barrero, J.L.: An improvement of the Euler–Chebyshev iterative method. J. Math. Anal. Appl. 315, 1–7 (2006) · Zbl 1113.65048
[5] Schröder, E.: Über unendlich viele Algorithmen zur Auflösung der Gleichungen. Math. Ann. 2, 317–365 (1870) · JFM 02.0042.02
[6] Grau-Sánchez, M., Grau, A., Noguera, M.: Frozen divided difference scheme for solving systems of nonlinear equations. J. Comput. Appl. Math. 235, 1739–1743 (2011) · Zbl 1204.65051
[7] Potra, F.A., Pták, V.: A generalization of Regula Falsi. Numer. Math. 36, 333–346 (1981) · Zbl 0478.65039
[8] Potra, F.A., Pták, V.: Nondiscrete Induction and Iterative Processes. Research Notes in Mathematics, vol. 103. Wiley, Boston–London–Melbourne (1984) · Zbl 0549.41001
[9] Polyanin, A.D., Manzhirov, A.V.: Handbook of Integral Equations. CRC Press, Boca Ratón (1998) · Zbl 0896.45001
[10] Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13, 87–93 (2000) · Zbl 0973.65037
[11] Chandrasekhar, D.: Radiative Transfer. Dover, New York (1960) · Zbl 0037.43201
[12] Argyros, I.K.: Quadratic equations and applications to Chandrasekhar’s and related equations. Bull. Aust. Math. Soc. 32(2), 275–292 (1985) · Zbl 0607.47063
[13] Argyros, I.K.: On a class of nonlinear integral equations arising in neutron transport. Aequ. Math. 35, 99–111 (1988) · Zbl 0657.45001
[14] Ezquerro, J.A., Gutiérrez, J.M., Hernández, M.A., Salanova, M.A.: Solving nonlinear integral equations arising in radiative transfer. Numer. Funct. Anal. Optim. 20, 661–673 (1999) · Zbl 0942.47043
[15] Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., Zimmermann, P.: MPFR: a multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Softw. 33(2), 15 (2007) · Zbl 1365.65302
[16] http://www.mpfr.org/mpfr-2.1.0/timings.html
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