A Highly Parallel Algorithm for Approximating All Zeros of a Polynomial with Only Real Zeros 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. CACM November, 1972 Patrick, M. L. parallel numerical algorithms, real polynomials, real zeros, Newton's method, starting values, guaranteed convergence 5.15 CA721103 JB January 27, 1978 2:35 PM 2266 5 2266 2266 5 2266 2266 5 2266 2660 5 2266 2266 6 2266