Average errors for zero finding: lower bounds for smooth or monotone functions.
Baker domains for Newton’s method
For an entire function let be the Newton function associated to . Each zero of is an attractive fixed point of and is contained in an invariant component of the Fatou set of the meromorphic function in which the iterates of converge to . If has an asymptotic representation , in a sector , then there exists an invariant component of the Fatou set where the iterates of tend to infinity. Such a component is called an invariant Baker domain.A question in the opposite direction...
Bemerkungen zum Verfahren der koordinatenweisen Suche
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.
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
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.
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
regularity of solutions of the Levi equation
Calcul de Weyl et opérateurs sous elliptiques
Calculation des valeurs numcute{e}riques des polynomes au moyen des spectres mathematiques
Caractérisation d'opérateurs pseudodifférentiels et applications (d'après R. Beals)
Cayley's problem
Newton's method for computation of a square root yields a difference equation which can be solved using the hyperbolic cotangent function. For the computation of the third root Newton's sequence presents a harder problem, which already Cayley was trying to solve. In the present paper two mutually inverse functions are defined in order to solve the difference equation, instead of the hyperbolic cotangent and its inverse. Several coefficients in the expansion around the fixed points are obtained,...
Chord Techniques and Newton's Method for Discrete Bifurcation Problems.
Chromatic roots of a ring of four cliques.