Using Optimization to Extract Roots of Real Coefficient Polynomials

[Claudio L.]

(07-12-2018 01:05 PM)Namir Wrote:  Finding the Durand-Kerner method was a real delightful surprise. I implemented the methods in both flavors--the Gauss-Seidel approach and the Jacobi approach. In the first approach, the updated guess for each root is used in updating the next roots (within each iteration). In the second approach, the updated roots are used in the next iteration.

Namir

I'm interested in the speed of this method, is it really faster than picking the roots one by one? When I needed a method to implement in newRPL, I didn't find this one but if it's really faster I'd like to see it implemented.
My other question is: does it have guaranteed convergence? or it may fail in some corner cases?
For newRPL I chose the Laguerre's method only because it will always converge to a root no matter how horrible your guess is. In my case this was important because the command that returns all the roots in a polynomial should work all the time, not just every now and then.
But if this method is always convergent and fast, I'm more than interested to replace it.