I am under the impression there are certain types of polynomials that root finders have trouble with. In other words, multiple real roots, complex roots very near to each other, etc. I am not interested in polynomials with order greater than 100.
I have been working on a new polynomial root finder and want to test it. I have bench marked it against Jenkins Traub, and do very well against that, but I am not sure that I am testing it with "difficult" polynomials.
My current test involves finding the roots of polynomials built with random coefficients, or building a polynomial from random roots (all real, all imaginary, all complex, or a mixture of these).
Is there any documentation that defines known problematic polynomials that can test the effectiveness of a root finder? Or can someone give some good testing guidelines for me to use?