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ParaStieltjes : Parallel computation of Gauss quadrature rules using a Parareal ‐like approach for the Stieltjes procedure
Author(s) -
Gander Martin J.,
Lunet Thibaut
Publication year - 2021
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2314
Subject(s) - gaussian quadrature , computation , mathematics , quadrature (astronomy) , gauss , gauss–jacobi quadrature , speedup , gauss–kronrod quadrature formula , clenshaw–curtis quadrature , algorithm , computer science , mathematical analysis , nyström method , integral equation , parallel computing , physics , engineering , quantum mechanics , electrical engineering
Summary The computation of Gauss quadrature rules for arbitrary weight functions using the Stieltjes algorithm is a purely sequential process, and the computational cost significantly increases when high accuracy is required. ParaStieltjes is a new algorithm to compute the recurrence coefficients of the associated orthogonal polynomials in parallel, from which the nodes and weights of the quadrature rule can then be obtained. ParaStieltjes is based on the time‐parallel Parareal algorithm for solving time‐dependent problems, and thus enlarges the applicability of this time parallel technique to a further, new area of scientific computing. We study ParaStieltjes numerically for different weight functions, and show that substantial theoretical speedup can be obtained when high accuracy is needed. We also present an asymptotic approximation for the node and weight distribution of Gauss quadrature rules, which can be used effectively in ParaStieltjes .