A New Initial Approximation Bound in the Durand Kerner Algorithm for Finding Polynomial Zeros
B.A. Sanjoyo, M. Yunus, N. Hidayat
Durand-Kerner算法是一种广泛使用的迭代技术,用于同时找到多项式的所有根源。 然而,它的收敛在很大程度上取决于初始近似值的选择。 本文介绍了两种用于确定初始值的新方法:新绑定1和lambda最大绑定,旨在提高算法的稳定性和收敛速度。 进行了理论分析和数值实验,以评估这些边界的有效性。 lambda最大绑定始终如一地确保所有根都位于复杂的圆圈内,导致更快,更稳定的收敛。 比较结果表明,虽然New bound 1保证收敛,但它产生过大的半径。
The Durand-Kerner algorithm is a widely used iterative technique for simultaneously finding all the roots of a polynomial. However, its convergence heavily depends on the choice of initial approximations. This paper introduces two novel approaches for determining the initial values: New bound 1 and the lambda maximal bound, aimed at improving the stability and convergence speed of the algorithm. Theoretical analysis and numerical experiments were conducted to evaluate the effectiveness of these ...