{"data":{"id":"10.4231/r7tb14tb","type":"dois","attributes":{"doi":"10.4231/r7tb14tb","prefix":"10.4231","suffix":"r7tb14tb","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":"OCVdM: Optimally conditioned Vandermonde matrices"}],"publisher":"Purdue University Research Repository","container":{},"publicationYear":2014,"subjects":[{"subject":"Computer Science"},{"subject":"Logarithmic weight functions"},{"subject":"Orthogonal polynomials"},{"subject":"Singular value decomposition"},{"subject":"Condition Numbers"},{"subject":"Vandermonde matrices"},{"subject":"Guassian Quadrature"},{"subject":"Matlab"},{"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/s10543-010-0293-1","resourceTypeGeneral":"JournalArticle","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["31 files","18 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;This software source code investigates numerically the extent to which the condition number of such matrices can be reduced, either by row-scaling or by optimal configurations of nodes. In the latter case we find empirically the condition of the optimally conditioned n \u0026amp;times; n Vandermonde matrix to grow exponentially at a rate slightly less than (1+\u0026lt;span class=\"_Tgc\"\u0026gt;\u0026amp;radic;2\u0026lt;/span\u0026gt;)^n.\u0026lt;/p\u0026gt;","descriptionType":"Abstract"},{"description":"Matlab routines for computing optimally conditioned Vandermonde matrices","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://purr.purdue.edu/publications/1573/1","contentUrl":null,"metadataVersion":11,"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":"2014-04-22T17:27:14.000Z","registered":"2014-04-22T17:27:15.000Z","published":"2014","updated":"2025-12-18T19:41:04.000Z"},"relationships":{"client":{"data":{"id":"purdue.purduelib","type":"clients"}},"provider":{"data":{"id":"purdue","type":"providers"}},"media":{"data":{"id":"10.4231/r7tb14tb","type":"media"}},"references":{"data":[]},"citations":{"data":[{"id":"10.1007/s10543-010-0293-1","type":"dois"}]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}