Title: Properties of Path Following Method for Roots of One Variable
Polynomials.
 
We study properties of one variable complex polynomials relevant to a
path following method.  Then we will study computational complexity of
the problem with respect to the choice of initial points and the step
size (a variable step size and a constant step size).
 
For a class of polynomials whose roots are in D_1(0), we will see that
the complexity of the problem improves as r gets close to 1, when when
choosing initial points on the circle S_r(0).