求多项式全部零点的异步并行算法

Asynchronous Parallel Algorithm for Finding All Zeros of a Polynomial

基于用圆盘算术求多项式全部零点的并行Halley迭代法虽然避免了颇为费事的圆盘开方运算 ,能同时求得多项式全部零点的带误差估计的近似值 ,并且具有很高的收敛速度 ,但它是同步并行算法。这里用圆盘算术构造了一种求多项式全部零点的异步并行算法 ,并在与Halley迭代法类似的条件下建立了它的收敛性定理。该算法不仅保持了Halley迭代法的优点 。

Parallel Halley iteration method, based on circular arithmetic for finding all zeros of a polynomial, avoids troublesome circular extraction operation,and the approximation with error estimation of all zeros of a polynomial can be obtained at the same time with it, and it has higher convergence rate , while it was synchronous parallel algorithm. The asynchronous parallel algorithm was constructed with circular arithmetic in order to find all zeros of a polynomial, and the convergence theory was established under the similar condition of Halley iteration method. The algorithm not only retain the advantage of Halley iteration method, but has better parallelism.