论文信息 - On Newton-type methods for multiple roots with cubic convergence

On Newton-type methods for multiple roots with cubic convergence

We introduce two families of Newton-type methods for multiple roots with cubic convergence. A further Newton-type method for multiple roots with cubic convergence is presented that is related to quadrature. We also provide numerical tests that show that these new methods are competitive to other known methods for multiple roots.

Herbert H. H. Homeier

[1] S. Rump. Ten methods to bound multiple roots of polynomials , 2003 .

[2] Naoki Osada,et al. An optimal multiple root-finding method of order three , 1994 .

[3] Beny Neta,et al. A higher order method for multiple zeros of nonlinear functions , 1983 .

[4] M. Frontini,et al. Modified Newton's method with third-order convergence and multiple roots , 2003 .

[5] Naoki Osada,et al. A one parameter family of locally quartically convergent zero-finding methods , 2007 .

[6] Naoki Osada,et al. Chebyshev-Halley methods for analytic functions , 2008 .

[7] Ernst Schröder,et al. Ueber unendlich viele Algorithmen zur Auflösung der Gleichungen , 1870 .

[8] Peter Kravanja,et al. A Modification of Newton's Method for Analytic Mappings Having Multiple Zeros , 1999, Computing.

[9] E. Hansen,et al. A family of root finding methods , 1976 .

[10] Naoki Osada,et al. Asymptotic error constants of cubically convergent zero finding methods , 2006 .

[11] J. Traub. Iterative Methods for the Solution of Equations , 1982 .

[12] Chen Dong,et al. A family of multiopoint iterative functions for finding multiple roots of equations , 1987 .