Are the coefficients of a polynomial well-conditioned functions of its roots?
Asymptotic Near Optimality of the Bisection Method.
Asymptotic-group analysis of algebraic equations.
Attractive Cycles in the Iteration of Meromorphic Functions.
Auswertungsverfahren für Polynome in mehreren Variablen.
Average errors for zero finding: Lower bounds.
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...
Bisection is not Optimal on the Average.
Bisection is Optimal
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.
Brève communication. Généralisation des extrapolations polynomiales et rationnelles
Calculation des valeurs numcute{e}riques des polynomes au moyen des spectres mathematiques
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,...
Circular Arithmetic and the Determination of Polynomial Zeros.
Complexity bound of absolute factoring of parametric polynomials.
Computational complexity. On the geometry of polynomials and a theory of cost. I
Computing quaternionic roots by Newton's method.
Concerning the rate of convergence of Newton's process
Congruence of analytic functions modulo a polynomial