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In this work, we study a global quadrature scheme for analytic functions oncompact intervals based on function values on quasi-uniform grids of quadraturenodes. In practice it is not always possible to sample functions at optimalnodes that give well-conditioned and quickly converging interpolatoryquadrature rules at the same time. Therefore, we go beyond classicalinterpolatory quadrature by lowering the degree of the polynomial approximantand by applying auxiliary mapping functions that map the original quadraturenodes to more suitable fake nodes. More precisely, we investigate thecombination of the Kosloff Tal-Ezer map and least-squares approximation (KTL)for numerical quadrature: a careful selection of the mapping parameter ensuresstability of the scheme, a high accuracy of the approximation and, at the sametime, an asymptotically optimal ratio between the degree of the polynomial andthe spacing of the grid. We will investigate the properties of this KTLquadrature and focus on the symmetry of the quadrature weights, the limitrelations for the mapping parameter, as well as the computation of thequadrature weights in the standard monomial and in the Chebyshev bases withhelp of a cosine transform. Numerical tests on equispaced nodes show that astatic choice of the map's parameter improve the results of the compositetrapezoidal rule, while a dynamic approach achieves larger stability and fasterconvergence, even when the sampling nodes are perturbed. From a computationalpoint of view the proposed method is practical and can be implemented in asimple and efficient way.

On Kosloff Tal-Ezer Least-Squares Quadrature Formulas