A globally convergent method for simultaneously finding polynomial roots

Pasquini, L.; Trigiante, D.

doi:10.1090/S0025-5718-1985-0771036-6

A globally convergent method for simultaneously finding polynomial roots
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by L. Pasquini and D. Trigiante PDF

Math. Comp. 44 (1985), 135-149 Request permission

Abstract:

A new method for the simultaneous approximation of all the roots of a polynomial is given. The method converges for almost every initial approximation, the set of the exceptional starting points being a closed set of measure zero, at least if all the polynomial roots are real and simple. The method exhibits quadratic convergence not only to simple, but also to multiple roots.

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