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 algori...
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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 differencealgorithm (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. (C) 2012 Elsevier Ltd. All rights reserved.
The quadrature method of moments (QMOM) has been widely used for the simulation of the evolution of moments of the aerosol general dynamic equations. However, there are several shortcomings in a crucial component of t...
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The quadrature method of moments (QMOM) has been widely used for the simulation of the evolution of moments of the aerosol general dynamic equations. However, there are several shortcomings in a crucial component of the method, the product-difference (P-D) algorithm. The P-D algorithm is used to compute the quadrature points and weights from the moments of an unknown distribution. The algorithm does not work for all types of distributions or for even reasonably high-order quadrature. In this work, we investigate the use of the Chebyshev algorithm and show that it is more robust than the P-D algorithm and can be used for a wider class of problems. The algorithm can also be used in a number of applications, where accurate computations of weighted integrals are required. We also illustrate the use of QMOM with the Chebyshev algorithm to solve several problems in aerosol science that could not be solved using the P-D algorithm. (C) 2011 Elsevier Ltd. All rights reserved.
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