摘要
秦九韶算法可以计算多项式函数在某点处的函数值,算法结构紧凑,计算量小,当计算多项式函数在某点处的导函数值时,需先求导再利用秦九韶算法计算.为了避免计算导数,同时可以减少计算量,于是提出新的迭代算法,即秦九韶改进算法.该算法可以直接计算多项式函数在某一点处的任意阶导数.同时将提出的秦九韶改进算法与Halley迭代算法相结合,可以更好地求解多项式代数方程.通过数值实验说明,与原Halley迭代算法相比,结合后的新算法收敛阶没有变化,但计算量少,所占内存小,效率指数高.
The Qin Jiushao Algorithm can calculate the function value of the polynomial at a certain point.The algorithm has compact structure and less computation.When calculating the derivative of the polynomial at the given point,the derivative must first be derived and then calculated using the Qin Jiushao Algorithm.In order to avoid calculating derivatives and reduce the amount of computation,the new iterative algorithm was proposed.It was Qin Jiushao Algorithm improved algorithm.The algorithm can directly calculate any derivative of the polynomial at this point.At the same time,the new iterative algorithm combined with Halley iteration algorithm,it can solve polynomial algebraic equations better.The numerical experiments show that compared with the original Halley iteration algorithm,the convergence order of the combined algorithm has not changed,but the computational complexity is less and the efficiency index is improved.
作者
常丑娥
CHANG Chou'e(Xinzhou Normal University Mathmatics Department,Xinzhou 034000,Shanxi,China)
出处
《山西师范大学学报(自然科学版)》
2025年第1期58-61,共4页
Journal of Shanxi Normal University(Natural Science Edition)
基金
山西省高等学校教学改革创新基金项目(J20220954)
2024年省级教改项目“数字赋能下数值分析与课程思政深度融合研究”(J20241267)
忻州师范学院院级教学改革创新基金项目(JGYB202218)。
