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Baker domains for Newton’s method

Walter Bergweiler, David Drasin, James K. Langley (2007)

Annales de l’institut Fourier

For an entire function $f$ let $N (z) = z - f (z) / f^{'} (z)$ be the Newton function associated to $f$ . Each zero $ξ$ of $f$ is an attractive fixed point of $N$ and is contained in an invariant component of the Fatou set of the meromorphic function $N$ in which the iterates of $N$ converge to $ξ$ . If $f$ has an asymptotic representation $f (z) \sim exp (- z^{n}), n \in ℕ$ , in a sector $| arg z | < ε$ , then there exists an invariant component of the Fatou set where the iterates of $N$ tend to infinity. Such a component is called an invariant Baker domain.A question in the opposite direction...

Bemerkungen zum Verfahren der koordinatenweisen Suche

Dieter Oelschlägel, Herbert Süsse (1981)

Aplikace matematiky

In der vorliegenden Arbeit wird das Verfahren der koordinatenweisen Suche mit Hilfe der Intervallarithmetik realisiert. Dadurch ist es möglich, bei speziellen nichtlinearen Optimierungsproblemen alle auftretenden Fehlerarten zu erfaßen, einschliesslich eingangsbedingter Fehler. Vor- und Nachteile werden erläutert sowie Testbeispiele angegeben.

Bifurcation of solutions of separable parameterized equations into lines.

Shen, Yun-Qiu, Ypma, Tjalling J. (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Bisection is not Optimal on the Average.

S. Graf, E. Novak, A. Papageorgiou (1987)

Numerische Mathematik

Bisection is Optimal

K. Sikorski (1982)

Numerische Mathematik

Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach.

Paluszny, Marco, Martín-Landrove, Miguel, Figueroa, Giovanni, Torres, Wuilian (2008)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Bordered augmented linear systems in numerical continuation and bifurcation.

W. Govaerts (1990/1991)

Numerische Mathematik

Boundary processes : the calculus of processes diffusing on the boundary

Carl Graham (1985)

Annales de l'I.H.P. Probabilités et statistiques

Bounds of the roots of the real polynomial

Imrich Komara (1987)

Aplikace matematiky

An algorithm for the calculation of a lower bound of the absolute values of the roots of a real algebraic polynomial, of an arbitrary degree, is derived. An example is given to compare the bounds calculated by the method proposed and by other methods.

Displaying 1 – 12 of 12

Baker domains for Newton’s method

Bemerkungen zum Verfahren der koordinatenweisen Suche

Bifurcation of solutions of separable parameterized equations into lines.

Bisection is not Optimal on the Average.

Bisection is Optimal

Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach.

Bordered augmented linear systems in numerical continuation and bifurcation.

Boundary processes : the calculus of processes diffusing on the boundary

Bounds of the roots of the real polynomial

Bounds on Nonlinear Operators in Finite-dimensional Banach Spaces.

Brève communication. Généralisation des extrapolations polynomiales et rationnelles

Brève communication. Résolution d’équations non linéaires de point fixe dans $𝐑^{n}$

Currently displaying 1 – 12 of 12