A note on determinantal representation of a Schröder–König-like simultaneous method for finding polynomial zeros
Tài liệu tham khảo
Petković, 1999, On rediscovered iteration methods for solving equations, J. Comput. Appl. Comp., 107, 275, 10.1016/S0377-0427(99)00105-3
Schröder, 1870, Über unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann., 2, 317, 10.1007/BF01444024
G.W. Stewart, On infinitely many algorithms for solving equations, http://drum.lib.umd.edu/handle/1903/577 (CS-TR-2990.ps), University of Maryland Library.
König, 1884, Über eine Eigenschaft der Potenzreiben, Math. Anal., 23, 447, 10.1007/BF01446400
Kalantari, 2009
Sakurai, 1991, A high-order iterative formula for simultaneous determination of zeros of a polynomial, J. Comput. Appl. Math., 38, 387, 10.1016/0377-0427(91)90184-L
Petković, 2007, Construction of zero-finding methods by Weierstrass functions, Appl. Math. Comput., 184, 351
Sakurai, 1966, On some simultaneous methods based on Weierstrass’ correction, J. Comput. Appl. Math., 72, 275, 10.1016/0377-0427(95)00278-2
Ehrlich, 1967, A modified Newton method for polynomials, Commun. ACM, 10, 107, 10.1145/363067.363115
Petković, 2005, A new-fourth order family of simultaneous methods for finding polynomial zeros, Appl. Math. Comput., 164, 227
Petković, 2008
Farmer, 2013
McNamee, 2007
Proinov, 2010, New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems, J. Complexity, 26, 3, 10.1016/j.jco.2009.05.001
Proinov, 2014, Semilocal convergence of Chebyshev-like root-finding method for simultaneous approximation of polynomial zeros, Appl. Math. Comput., 236, 669
Proinov, 2016, On the local convergence of Ehrlich method for numerical computation of polynomial zeros, Calcolo, 53, 413, 10.1007/s10092-015-0155-y
Bini, 2000, Design, analysis and the implementation of a multiprecision polynomial rootdinder, Numer. Algorithms, 23, 127, 10.1023/A:1019199917103
Z. Zeng, A method computing multiple roots of inexact polynomials, in: ISSAC Proceedings of the International Symposium on Symbolic and Algebraic Computation, Philadelphia, 2003, pp. 266–272.
Farmer, 2017, Iteration functions re-visited, J. Comput. Appl. Math., 311, 484, 10.1016/j.cam.2016.08.021
Householder, 1953
Hamilton, 1946, Roots of equations by functional iteration, Duke Math. J., 13, 113, 10.1215/S0012-7094-46-01312-9
Petković, 2010, On Schröder’s families of root-finding methods, J. Comput. Appl. Math., 233, 1755, 10.1016/j.cam.2009.09.012
Nourein, 1977, An improvement on two iteration methods for simultaneous determination of the zeros of a polynomial, Int. J. Comput. Math., 6, 241, 10.1080/00207167708803141
Sakurai, 1991, An iterative method for algebraic equation by Padé approximation, Computing, 46, 131, 10.1007/BF02239167
Leslie, 1991, How not to repeatedly differentiate a reciprocal, Amer. Math. Monthly, 98, 732, 10.1080/00029890.1991.11995782