On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM)

Three methods are reviewed for computing optimal weights and abscissas which can be used in the quadrature method of moments (QMOM): the product-difference algorithm (PDA), the long quotient-modified difference algorithm (LQMDA, variants are also called Wheeler algorithm or Chebyshev algorithm), and the Golub–Welsch algorithm (GWA). The PDA is traditionally used in applications. It is discussed that the PDA fails in certain situations whereas the LQMDA and the GWA are successful. Numerical studies reveal that the LQMDA is also more efficient than the PDA.

► The QMOM needs to find optimal quadrature rules over and over again.
► Three methods are reviewed for computing optimal weights and abscissas.
► The product-difference algorithm is traditionally used in applications.
► The long quotient-modified difference algorithm turns out to be more robust and efficient.