Abstract
We propose an algorithm to find a starting point for iterative methods. Numerical experiments show empirically that the algorithm provides starting points for different iterative methods (like Newton method and its variants) with low computational cost.
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References
Maruster, S.: The solution by iteration of nonlinear equations in Hilbert spaces. Proc. Amer. Math. Soc. 63, 69–73 (1977)
Baker Kearfott, R.: Abstract generalized bisection and cost bound. Math. Comput. 49(179), 187–202 (1987)
Adler, A.: On the bisection method for triangles. Math. Comput. 40(162), 571–574 (1983)
Xu, Z.-B., Zhang, J.-S., Wang, W.: A cell exclusion algorithm for determining all the solutions of a nonliniar system of equations. Appl. Math. and Comput. 80, 181–208 (1996)
Hansen, E.R., Greenberg, R.I.: An interval Newton method. Appl. Math. Comput. 12(2-3), 89–98 (1983)
Allgower, E.L., Georg, K.: Simplicial and continuation methods for approximating fixed points and solutions to systems of equations. SIAM Rev. 22, 28–85 (1980)
Karra, C.L., Weckb, B., Freemanc, L.M.: Solutions to systems of nonlinear equations via a genetic algorithm. Eng. Appl. Artif. Intel. 11(3), 369–376 (1998)
Rheinboldt, W.C.: An adaptive continuation process for solving systems of nonlinear equations. Polish Acad. Sci. Banach Center Publ. 3, 129–14 (1975)
Catinas, E.: Estimating the radius of an attraction ball. Appl. Math. Lett. 22, 712–714 (2009)
Hernández-Veron, M.A., Romero, N.: On the local convergence of a third order family of iterative processes. Algorithms 8, 1121–1128 (2015)
Rus, I.A.: A conjecture on global asymptotic stability, workshop iterative approximation of fixed points. In: 19Th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara (2017)
Berinde, V., Maruşter, St., Rus, I.A.: On an open problem regarding the spectral radius of the derivatives of a function and of its iterates (in preparation)
Miyajima, S., Kashiwagi, M.: Existence test for solution of nonlinear systems applying affine arithmetic. J. Comput. Appl. Math. 199, 304–309 (2007)
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Ştefan Măruşter is deceased.
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Măruşter, Ş., Măruşter, L. On the problem of starting points for iterative methods. Numer Algor 81, 1149–1155 (2019). https://doi.org/10.1007/s11075-018-0589-9
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DOI: https://doi.org/10.1007/s11075-018-0589-9