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A family of root finding methods. (English) Zbl 0361.65041

65H05Single nonlinear equations (numerical methods)
Full Text: DOI EuDML
[1] Traub, J. F.: Iterative methods for the solution of equations. New York: Prentice-Hall 1964 · Zbl 0121.11204
[2] Ostrowski, A. M.: Solution of equations and systems of equations. 3rd ed. New York-London: Academic Press 1973 · Zbl 0304.65002
[3] Davies, M., Dawson, B.: On the global convergence of Halley’s iteration formula. Num. Math.24, 133-135 (1975) · Zbl 0313.65037 · doi:10.1007/BF01400962
[4] Parlett, B.: Laguerre’s method applied to the matrix eigenvalue problem. Math. Comp.18, 464-485 (1964) · Zbl 0124.33004
[5] Kahan, W.: Where does Laguerre’s method come from? Fourth Annual Princeton Conference on Information Sciences and Systems (1970)
[6] Bodewig, E.: Sur la méthode Laguerre pour l’approximation des racines de certaines équations algébriques et sur la critique d’Hermite. Indag. Math.8, 570-580 (1946)
[7] Laguerre, E. N.: Oeuvres de Laguerre, Vol. 1, pp. 87-103
[8] Dordevi?, L. N.: An iterative solution of algebraic equations with a parameter to accelerate convergence. Univ. Beograd. Publ. Elektrotechn. Fak. Ser. Mat. Fiz., # 449, pp. 179-182 (1973) · Zbl 0282.65040
[9] Tihonov, O. N.: On the rapid computation of the largest zeros of a polynomial [Russian]. Zap. Leningrad. Gorn. In-ta48, No. 3, 36-41 (1968)