Application of Parallel Computing to Obtain all Real Solutions of a High Degree Univariate Polynomial Equation

Abstract

Solving the high order equation to get the complex roots is of great importance for analysis and synthesis of the engineering projects. A few methods, such as the Optimal Trinomial Factor method and the Splitting Trinomial Factor method, can be used to solve these equations. However, these methods may not converge. In addition, as they have computing residuals optimizing a trinomial factor of the algebra equation, it has an influence on the accuracy of the calculation. To solve the shortcomings of the traditional method, a parallel method for solving the complex roots of a high order equation is proposed, which has combined the genetic algorithm and parallel computing. This method uses its strong global convergence and better optimization ability. In determining the appropriate initial population and scale, the method can be used to obtain all the complex roots quickly and efficiently. The results of numerical experiments show the validity and convergence of the proposed method, and obtain the full number of roots of the equation to ensure the accuracy of the calculation results.