Abstract The computation of n -point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It shown that the nodes and weights rule can be retrieved from singular value decomposition a bidiagonal matrix size /2. proposed numerical method allows to compute with high relative accuracy computational complexity $ \mathcal {O} (n^{2}). <mml:math xmlns:mml="http://www....

Abstract We analyse the Gaussian wave packet transform. Based on Fourier inversion formula and a partition of unity, which is formed by collection basis functions, new representation square-integrable functions presented. Including rigorous error analysis, variants transform are then derived discretization integral via different quadrature rules. Gauss–Hermite quadrature, we introduce packets i...