The globalization of Durand-Kerner algorithm

Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory