×
Neuberger, J. W.

Continuous Newton’s method for polynomials. (English) Zbl 1052.30502

Math. Intell. 21, No. 3, 18-23 (1999).
From the text: A description of domains of attraction for the continuous Newton method for a polynomial \(p\) is given using an improved version of the latter method. The differential equation \(p(z)'=-p(z)\) rather than \(p'(z)z'=-p(z)\) is being used.

Cited in 14 Documents

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
PDF BibTeX XML Cite
\textit{J. W. Neuberger}, Math. Intell. 21, No. 3, 18--23 (1999; Zbl 1052.30502)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] J.M. Ball, Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations,Nonlinear Sci. 7 (1997), 475–502. · Zbl 0903.58020
[2] F. von Haeseler and H. Kriete, The relaxed Newton’s method for rational functions.Random Computat. Dynam. 3 (1995), 71–92. · Zbl 0839.58034
[3] H. Jongen, P. Jonker, and F. Twilt, The continuous, desingularized Newton method for meromorphic functions,Acta Appl. Math. 13 (1988), 81–121. · Zbl 0701.58031
[4] J.W. Neuberger,Sobolev Gradients and Differential Equations, Springer Lecture Notes in Mathematics Vol. 1670, Springer-Verlag, New York, 1997. · Zbl 0935.35002
[5] H. Peitgen, M. Prufer, and K. Schmitt, Global aspects of the continuous and discrete Newton method: A case study,Acta Appl. Math. 13 (1988), 123–202. · Zbl 0669.65038
[6] D. Saupe, Discrete versus continuous Newton’s method: A case study,Acta Appl. Math. 13(1988), 59–80. · Zbl 0669.65037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.