Batra, PrashantPrashantBatra2021-02-232021-02-232002-09-01BIT Numerical Mathematics 42 (3): 467-476 (2002-09-01)http://hdl.handle.net/11420/8918Beside 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.en0006-383520023467476Convergence theoremsNewton iterationPoint estimatesPolynomial rootsPractical conditions for convergenceSimultaneous methodsMathematikJournal ArticleOther