{"data":{"id":"10.4231/r71v5bw8","type":"dois","attributes":{"doi":"10.4231/r71v5bw8","prefix":"10.4231","suffix":"r71v5bw8","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Gautschi, Walter","givenName":"Walter","familyName":"Gautschi","affiliation":["Purdue University"],"nameIdentifiers":[{"schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0000-0001-9184-8899","nameIdentifierScheme":"ORCID"}]}],"titles":[{"title":"HPGT: High-precision Gauss-Turan quadrature rules"}],"publisher":"Purdue University Research Repository","container":{},"publicationYear":2014,"subjects":[{"subject":"Computer Science"},{"subject":"Orthogonal polynomials"},{"subject":"Variable-precision arithmetic"},{"subject":"Laguerre weight functions"},{"subject":"Matlab"},{"subject":"Gauss-type quadrature rules"},{"subject":"Hermite weight function"},{"subject":"Software source code"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Walter Gautschi Archives"}],"contributors":[],"dates":[{"date":"2014-04-22","dateType":"Available"},{"date":"2014-04-22","dateType":"Submitted"},{"date":"2014-04-23","dateType":"Accepted"},{"date":"2014","dateType":"Issued"}],"language":"en","types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Datasets","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"10.1007/s11075-013-9774-z","resourceTypeGeneral":"JournalArticle","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["17 files","16 KB"],"formats":["text/html","text/plain"],"version":"1.0","rightsList":[{"rights":"Creative Commons Zero v1.0 Universal","rightsUri":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc0-1.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"\u0026lt;p\u0026gt;Matlab software are presented for generating Gauss\u0026amp;ndash;Tur\u0026amp;aacute;n quadrature rules for the Laguerre and Hermite weight functions to arbitrarily high accuracy. This is accomplished by the Newton\u0026amp;ndash;Kantorovich method, using initial approximations that are sufficiently accurate to be capable of producing n-point quadrature formulae for n as large as 42 in the case of the Laguerre weight function, and 90 in the case of the Hermite weight function.\u0026lt;/p\u0026gt;","descriptionType":"Abstract"},{"description":"Matlab routines that calculate high-precision Gauss-Turan quadrature rules","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://purr.purdue.edu/publications/1580/1","contentUrl":null,"metadataVersion":9,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":1,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2014-04-22T17:36:43.000Z","registered":"2014-04-22T17:36:44.000Z","published":"2014","updated":"2025-12-18T19:41:08.000Z"},"relationships":{"client":{"data":{"id":"purdue.purduelib","type":"clients"}},"provider":{"data":{"id":"purdue","type":"providers"}},"media":{"data":{"id":"10.4231/r71v5bw8","type":"media"}},"references":{"data":[{"id":"10.1007/s11075-013-9774-z","type":"dois"}]},"citations":{"data":[]},"parts":{"data":[]},"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