On Kosloff Tal-Ezer least-squares quadrature formulas

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