论文标题
高斯的快速可靠的高精度计算 - 雅各比正交
Fast and reliable high accuracy computation of Gauss--Jacobi quadrature
论文作者
论文摘要
描述了具有认证收敛的迭代方法，用于计算高斯 - 雅各比四倍。这些方法不需要对节点的先验估计来保证其四阶收敛。它们通常比以前的方法更快，并且在参数范围内没有实际限制。对二次的节点和权重的评估仅基于收敛过程，这些过程以及计算节点的固定点方法的第四阶收敛，使这是用于高精度计算的理想方法，以至于在典型的典型laptops中，即使是数百万个节点和数以千计的数字计算，甚至数千个节点和数以千计的数字都可以计算。
Iterative methods with certified convergence for the computation of Gauss--Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be generally faster than previous methods and without practical restrictions on the range of the parameters. The evaluation of the nodes and weights of the quadrature is exclusively based on convergent processes which, together with the fourth order convergence of the fixed point method for computing the nodes, makes this an ideal approach for high accuracy computations, so much so that computations of quadrature rules with even millions of nodes and thousands of digits are possible in a typical laptop.
