摘要
探讨Legendre正交多项式的性质并给出它关于n奇偶性的通项表示.通过n个零点及其对称性,借助配方多项式,建立配方系数与通项系数的对应关系,构造配方系数的非线性方程组.最后,用拟牛顿法求解配方系数,求得Legendre多项式的n个零点和对应的求积系数,降低零点求解的复杂度,方便了Gauss型求积公式的应用.
The nature of the Legendre orthogonal polynomials and a common expression about n parity are discussed in this paper. By using of Legendre orthogonal polynomials n zero＇ s symmetry and poly-nomial formula, the formula coefficients and the corresponding coefficients are established in the rela- tionship between structure formula coefficients of nonlinear equations. Making use of the final quasi - Newton method for solving formula coefficients, the n - zero of sponding quadrature Legendre polynomials and the corre-coefficients are obtained. Our results efficiently reduce the complexity of solving zeros of Legendre polynomials for the Gauss quadrature formula.
出处
《福州大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第3期334-338,共5页
Journal of Fuzhou University(Natural Science Edition)
基金
福建省教育厅科研资助项目(JB08027
JB08026)
福州大学研究生教育研究资助项目(09AY09)
