2018/11/12 by Pierre-David Létourneau, Létourneau, Pierre-David, Eric Darve +1
Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Nuclear Physics and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1811.04846
openalex publication_date 2018/11/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We introduce a new type of quadrature, known as approximate Gaussian quadrature (AGQ) rules using ε-quasiorthogonality, for the approximation of integrals of the form ∫ f(x)d α(x). The measure α(⋅) can be arbitrary as long as it possesses finite moments μn for sufficiently large n. The weights and nodes associated with the quadrature can be computed in low complexity and their count is inferior to that required by classical quadratures at fixed accuracy on some families of integrands. Furthermore, we show how AGQ can be used to discretize the Fourier transform with few points in order to obtain short exponential representations of functions.