{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T19:29:41Z","timestamp":1698780581670},"reference-count":33,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2020,6,29]],"date-time":"2020-06-29T00:00:00Z","timestamp":1593388800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,5]]},"abstract":"Summary<\/jats:title>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<\/jats:sc> 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<\/jats:sc> is based on the time\u2010parallel Parareal<\/jats:sc> algorithm for solving time\u2010dependent problems, and thus enlarges the applicability of this time parallel technique to a further, new area of scientific computing. We study ParaStieltjes<\/jats:sc> 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<\/jats:sc>.<\/jats:p>","DOI":"10.1002\/nla.2314","type":"journal-article","created":{"date-parts":[[2020,6,30]],"date-time":"2020-06-30T06:09:44Z","timestamp":1593497384000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["ParaStieltjes<\/scp>: Parallel computation of Gauss quadrature rules using a Parareal<\/scp>\u2010like approach for the Stieltjes procedure"],"prefix":"10.1002","volume":"28","author":[{"given":"Martin J.","family":"Gander","sequence":"first","affiliation":[{"name":"Section of Mathematics University of Geneva Canton of Geneva Switzerland"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-1745-0780","authenticated-orcid":false,"given":"Thibaut","family":"Lunet","sequence":"additional","affiliation":[{"name":"Section of Mathematics University of Geneva Canton of Geneva Switzerland"}]}],"member":"311","published-online":{"date-parts":[[2020,6,29]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964806060013"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4073(00)00026-1"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/174603.174605"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-23321-5_3"},{"key":"e_1_2_8_6_1","doi-asserted-by":"crossref","unstructured":"LecouvezM FalgoutRD WoodwardCS TopP. 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