{"data":{"id":"10.4231/r7pk0d31","type":"dois","attributes":{"doi":"10.4231/r7pk0d31","prefix":"10.4231","suffix":"r7pk0d31","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":"NUMINT: Numerical Integration over the square"}],"publisher":"Purdue University Research Repository","container":{},"publicationYear":2014,"subjects":[{"subject":"Computer Science"},{"subject":"Gauss quadrature approximation"},{"subject":"Gaussian quadrature"},{"subject":"Orthogonal polynomials"},{"subject":"Numerical integration over the square"},{"subject":"Aerodynamical drag coefficient"},{"subject":"Matlab"},{"subject":"Walter Gautschi Selected Works"},{"subject":"Quadrature and cubature formulas"},{"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":"IsReferencedBy","relatedIdentifier":"10.1007/s11075-012-9611-9","resourceTypeGeneral":"JournalArticle","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["20 files","8 KB"],"formats":["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;Tensor-product formulae based on one-dimensional Gaussian quadratures are developed for evaluating double integrals of the type indicated in the title. If the singularities occur only along the diagonal and the regular part of the integrand is a polynomial of total degree \u0026amp;#39;\u0026amp;#39;d\u0026amp;#39;\u0026amp;#39;, the formulae can be made exact by choosing the number of quadrature points larger than, or equal to, 1 + \u0026amp;#39;\u0026amp;#39;d\u0026amp;#39;\u0026amp;#39;/2.\u0026lt;/p\u0026gt;","descriptionType":"Abstract"},{"description":"Matlab routines for computing numerical integration over the square","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://purr.purdue.edu/publications/1575/1","contentUrl":null,"metadataVersion":6,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":1,"citationsOverTime":[{"year":"2025","total":1}],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2014-04-22T17:29:51.000Z","registered":"2014-04-22T17:29:52.000Z","published":"2014","updated":"2025-12-18T19:41:06.000Z"},"relationships":{"client":{"data":{"id":"purdue.purduelib","type":"clients"}},"provider":{"data":{"id":"purdue","type":"providers"}},"media":{"data":{"id":"10.4231/r7pk0d31","type":"media"}},"references":{"data":[]},"citations":{"data":[{"id":"10.1007/s11075-012-9611-9","type":"dois"}]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}