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

The efficient method, which combines the advantages of parallel computing and golden section, is put forward to solve a high degree univariate polynomial equation. This method can be used to overcome the shortcomings of common methods, which need to good initial values and may omit part of real solutions. Firstly, a simulation algorithm are provided. The golden section method is used to reduce the number of iterations and the parallel computing can efficiency calculate the solutions. Then, the stability and convergence of the method are strictly proved. Finally, numerical computations are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solutions and obtain all the real solutions of the equation. The approach has high convergence rate and precision. It can be applied to the large scale problems arising from scientific and engineering computing.