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An improvement to Ostrowski root-finding method. (English) Zbl 1090.65053
Summary: An improvement to the iterative method based on the Ostrowski one to compute nonlinear equation solutions, which increases the local order of convergence is suggested. The adaptation of a strategy presented here gives a new iteration function with an additional evaluation of the function. It also shows a smaller cost if we use adaptive multi-precision arithmetic. The numerical results computed using this system with a floating point system representing 200 decimal digits support this theory.

65H05Single nonlinear equations (numerical methods)
Algorithm 719
Full Text: DOI
[1] Ostrowski, A. M.: Solutions of equations and system of equations. (1960) · Zbl 0115.11201
[2] Grau, M.; Noguera, M.: A variant of Cauchy’s method with accelerated fifth-order convergence. Applied mathematics letter 17, 509-517 (2004) · Zbl 1070.65034
[3] Grau, M.: An improvement to the computing of nonlinear equation solutions. Numerical algorithms 34, 1-12 (2003) · Zbl 1043.65071
[4] Betounes, D.; Redfern, M.: Mathematical computing. (2002) · Zbl 0984.68031
[5] Garvan, F.: The Maple book. (2001) · Zbl 1005.68185
[6] Alefeld, G. E.; Potra, F. A.: Some efficient methods for enclosing simple zeros of nonlinear equations. Bit 32, 334-344 (1992) · Zbl 0756.65070
[7] Costabile, F.; Gualtieri, M. I.; Luceri, R.: A new iterative method for the computation of the solutions of nonlinear equations. Numerical algorithms 28, 87-100 (2001) · Zbl 0991.65045
[8] Stoer, J.; Bulirsch, R.: Introduction to numerical analysis. (1983) · Zbl 0771.65002
[9] Traub, J. F.: Iterative methods for the solution of equations. (1964) · Zbl 0121.11204
[10] Bailey, D. H.: Multiprecision translation and execution of Fortran programs. ACM transactions on mathematical software 19, No. 3, 288-319 (1993) · Zbl 0889.68015