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    Item type:Publication, Access status: without files ,
    Simultaneous point estimates for Newton's method
    (2002-09-01)
    Batra, Prashant
    Beside the classical Kantorovich theory there exist convergence criteria for the Newton iteration which only involve data at one point, i.e. point estimates. Given a polynomial P, these conditions imply the point evaluation of n = deg(P) functions (from a certain Taylor expansion). Such sufficient conditions ensure quadratic convergence to a single zero and have been used by several authors in the design and analysis of robust, fast and efficient root-finding methods for polynomials. In this paper a sufficient condition for the simultaneous convergence of the one-dimensional Newton iteration for polynomials will be given. The new condition involves only n point evaluations of the Newton correction and the minimum mutual distance of approximations to ensure "simultaneous" quadratic convergence to the pairwise distinct n roots.
    Publicationtype: Journal Article
      45
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    Improvement of a convergence condition for the Durand-Kerner iteration
    (Elsevier, 1998-09-15)
    Batra, Prashant
    The Durand-Kerner iteration is a well-known simultaneous method for approximation of (simple) zeros of a polynomial. By relating Weierstrass' correction and the minimal distance between approximations practical conditions for convergence have been obtained. These conditions also ensure the existence of isolating discs for the polynomial roots, i.e. each iteration step gives a refined set of inclusion discs. In this paper refined conditions of convergence are given.
    Publicationtype: Journal Article
      39