在工程数值计算、X射线衍射线形分析、光谱学等领域常使用高斯数值积分，高斯积分的节点及权重因子是数值积分的必须数据。研究了高次勒让德、拉盖尔和厄米多项式的零 点，即高斯-勒让德、高斯-拉盖尔、高斯-厄米积分的节点的计算方法，给出了一种有效的高精度数值算法——搜索迭代方法（scan-iteration method，SIM）。根据勒让德、拉盖尔、厄米多项式的特点，对拉盖尔多项式、厄米多项式的定义稍做变化后，获得了计算多项 式值的稳定递推关系。求它们的根时，先在一定范围内以一定的步长搜索根所在的

Gauss quadrature is used widely in many fields such as the engineering numerical computation, X-ray diffraction profile analysis, spectroscopy,and so on. The nodes and weight factors of Gauss-quadrature are essential data to the numerical integration. A method to compute the zeroes of the high-degree Legendre, Laguerre and Hermite polynomials, which are the nodes of Gauss-Legendre, Gauss-Laguerre and Gauss-Hermite Quadrature, respectively, is studied, and a very efficient algorithm scan-iteration method(SIM) is given. According to the properties of Legendre, Laguerre and Hermite polynomials, their definitions are modified a little, and the stable recursive relations to compute their value are obtained. To extract these polynomials, their root intervals are searched with a certain step within a certain range. After the intervals of all roots are obtained, the roots with the desired precision can be gotten by the general iteration methods such as secant or bisection method. Numerical experiments indicate that the method is very efficient and the high-precise roots of Legendre, Laguerre and Hermite polynomials can be extracted.