THE GLOBALIZATION OF DURAND-KERNER ALGORITHM

Making use of the theory of continuous homotopy and the relation betwe en symmetric polynomial and polynomial in one variable the authors dev oted this article to constructing a regularly homotopic curve with pro bability one. Discrete tracing along this homotopic curve leads to a c lass of Durand-Kerner algorithm with step parameters. The convergence of this class of algorithms is given, which solves the conjecture abou t the global property of Durand-Kerner algorithm. The problem for step length selection is thoroughly discussed. Finally, sufficient numerica l examples are used to verify our theory.