A highly parallel algorithm for approximating all zeros of a polynomial with only real zeros

Authors:
Merrell L. Patrick
Affiliations:
Duke Univ., Durham, NC
Venue:
Communications of the ACM
Year:
1972

Citing 1
Cited 3

Parallel numerical methods for the solution of equations

Communications of the ACM

Addendum to M.L. Patrick paper

Communications of the ACM
Analysis of Asynchronous Polynomial Root Finding Methods on a Distributed Memory Multicomputer

IEEE Transactions on Parallel and Distributed Systems
A two-steps algorithm for approximating real roots of a polynomial in Bernstein basis

Mathematics and Computers in Simulation

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Abstract

An algorithm is described based on Newton's method which simultaneously approximates all zeros of a polynomial with only real zeros. The algorithm, which is conceptually suitable for parallel computation, determines its own starting values so that convergence to the zeros is guaranteed. Multiple zeros and their multiplicity are readily determined. At no point in the method is polynomial deflation used.