In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on arbitrary grids of quadrature nodes. In practice it is not always possible to sample functions at optimal nodes with a low-order Lebesgue constant. Therefore, we go beyond classical interpolatory quadrature by lowering the degree of the polynomial approximant and by applying auxiliary mapping functions that map the original quadrature nodes to more suitable fake nodes. More precisely, we investigate the combination of the Kosloff Tal-Ezer map and Least-squares approximation (KTL) for numerical quadrature: a careful selection of the mapping parameter $\alpha$ ensures a high accuracy of the approximation and, at the same time, an asymptotically optimal ratio between the degree of the polynomial and the spacing of the grid. We will investigate the properties of this KTL quadrature and focus on the symmetry of the quadrature weights, the limit relations for $\alpha$ converging to $0^{+}$ and $1^{-}$, as well as the computation of the quadrature weights in the standard monomial and in the Chebyshev bases with help of a cosine transform. Numerical tests on equispaced nodes show that some static choices of the map's parameter improve the results of the composite trapezoidal rule, while a dynamic approach achieves larger stability and faster convergence, even when the sampling nodes are perturbed. From a computational point of view the proposed method is practical and can be implemented in a simple and efficient way.

翻译：在这项工作中,我们根据二次节点任意网格上的功能值,研究一个全球在压缩间隔中分析函数的二次图解机制。 在实践上,我们并不总是能够以低阶 Lebesgue 常量在最佳节点上取样功能。 因此,我们超越了传统的跨度二次图,降低了多元相近度和电网间距之间的比例,并应用了辅助绘图功能,将原二次点映射到更合适的假节点。 更准确地说,我们调查了Kosloff Tal- Ezer 地图和最小平方对数值的趋同值调和最小方位调合值的结合。 仔细选择绘图参数 $\ ALpha$ 会确保高的近度, 同时,我们会超越典型间隙间隙间隙, 绘制原二次点结节点的对比值, 并关注二次曲线重量的对等值的对等值的对称性选择, 更实际的调和最低平面值的对数值对数值对数值的对比, 以美元为基调值为平价, 以平价计算为基调, 以平价计算, 以平价计算为基底的比值为基底的比值为基底为基底,, 以10值, 和基底的比值为基底的对值, 和基底的对比值为基底的对价,,,, 基底的变值为基底的对值和基底的比值为基底的对值为基底的对价,,,,, 。