COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA
We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. T...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on numerical analysis 2010-01, Vol.48 (5), p.1984-1999 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1999 |
|---|---|
| container_issue | 5 |
| container_start_page | 1984 |
| container_title | SIAM journal on numerical analysis |
| container_volume | 48 |
| creator | BOS, L. DE MARCHI, S. SOMMARIVA, A. VIANELLO, M. |
| description | We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes. |
| doi_str_mv | 10.1137/090779024 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_miscellaneous_901712871</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>41149034</jstor_id><sourcerecordid>41149034</sourcerecordid><originalsourceid>FETCH-LOGICAL-c411t-6279ac8e9feeef7f407aaede9c9853150e3a2fb952c069341879ec62919a20e13</originalsourceid><addsrcrecordid>eNpd0MFKw0AQBuBFFKzVgw8gLF7EQ3RmN8lmj9u6rdE0LTERPIUYN9DSNjXbHnx7t1R68DQMfPzM_IRcIzwgcvEIEoSQwPwT0kOQgSdQwCnpAfDQQ5_Jc3Jh7QLcHiHvkXg4ncyKPE7HdFIkefyusljlmo70q3ZDpU800S-KzqZxmr_RwQdNi4nO4qFKaBKnWmVUJWM9yNQlOWuqpTVXf7NPipHOh89eMh3vuVf7iFsvZEJWdWRkY4xpROODqCrzZWQto4BjAIZXrPmUAashlNzHSEhTh0yirBgY5H1yd8jddO33zthtuZrb2iyX1dq0O1tKQIEsEnt5-08u2l23dseVLlQwziU4dH9Addda25mm3HTzVdX9lAjlvtLyWKmzNwe7sNu2O0L3l--SfP4LnTZpOA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>879723390</pqid></control><display><type>article</type><title>COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA</title><source>SIAM Journals Online</source><source>JSTOR Mathematics & Statistics</source><source>JSTOR</source><creator>BOS, L. ; DE MARCHI, S. ; SOMMARIVA, A. ; VIANELLO, M.</creator><creatorcontrib>BOS, L. ; DE MARCHI, S. ; SOMMARIVA, A. ; VIANELLO, M.</creatorcontrib><description>We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.</description><identifier>ISSN: 0036-1429</identifier><identifier>EISSN: 1095-7170</identifier><identifier>DOI: 10.1137/090779024</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Algorithms ; Approximation ; Asymptotic methods ; Asymptotic properties ; Cardinality ; Computer programs ; Determinants ; Factorization ; Greedy algorithms ; Interpolation ; Linear algebra ; Mathematical analysis ; Matrices ; Numerical analysis ; Numerical linear algebra ; Polynomials ; Studies</subject><ispartof>SIAM journal on numerical analysis, 2010-01, Vol.48 (5), p.1984-1999</ispartof><rights>Copyright ©2011 Society for Industrial and Applied Mathematics</rights><rights>Copyright Society for Industrial and Applied Mathematics 2010</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c411t-6279ac8e9feeef7f407aaede9c9853150e3a2fb952c069341879ec62919a20e13</citedby><cites>FETCH-LOGICAL-c411t-6279ac8e9feeef7f407aaede9c9853150e3a2fb952c069341879ec62919a20e13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/41149034$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/41149034$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,3184,27924,27925,58017,58021,58250,58254</link.rule.ids></links><search><creatorcontrib>BOS, L.</creatorcontrib><creatorcontrib>DE MARCHI, S.</creatorcontrib><creatorcontrib>SOMMARIVA, A.</creatorcontrib><creatorcontrib>VIANELLO, M.</creatorcontrib><title>COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA</title><title>SIAM journal on numerical analysis</title><description>We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Cardinality</subject><subject>Computer programs</subject><subject>Determinants</subject><subject>Factorization</subject><subject>Greedy algorithms</subject><subject>Interpolation</subject><subject>Linear algebra</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Numerical analysis</subject><subject>Numerical linear algebra</subject><subject>Polynomials</subject><subject>Studies</subject><issn>0036-1429</issn><issn>1095-7170</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNpd0MFKw0AQBuBFFKzVgw8gLF7EQ3RmN8lmj9u6rdE0LTERPIUYN9DSNjXbHnx7t1R68DQMfPzM_IRcIzwgcvEIEoSQwPwT0kOQgSdQwCnpAfDQQ5_Jc3Jh7QLcHiHvkXg4ncyKPE7HdFIkefyusljlmo70q3ZDpU800S-KzqZxmr_RwQdNi4nO4qFKaBKnWmVUJWM9yNQlOWuqpTVXf7NPipHOh89eMh3vuVf7iFsvZEJWdWRkY4xpROODqCrzZWQto4BjAIZXrPmUAashlNzHSEhTh0yirBgY5H1yd8jddO33zthtuZrb2iyX1dq0O1tKQIEsEnt5-08u2l23dseVLlQwziU4dH9Addda25mm3HTzVdX9lAjlvtLyWKmzNwe7sNu2O0L3l--SfP4LnTZpOA</recordid><startdate>20100101</startdate><enddate>20100101</enddate><creator>BOS, L.</creator><creator>DE MARCHI, S.</creator><creator>SOMMARIVA, A.</creator><creator>VIANELLO, M.</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope><scope>7SC</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20100101</creationdate><title>COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA</title><author>BOS, L. ; DE MARCHI, S. ; SOMMARIVA, A. ; VIANELLO, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c411t-6279ac8e9feeef7f407aaede9c9853150e3a2fb952c069341879ec62919a20e13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Asymptotic methods</topic><topic>Asymptotic properties</topic><topic>Cardinality</topic><topic>Computer programs</topic><topic>Determinants</topic><topic>Factorization</topic><topic>Greedy algorithms</topic><topic>Interpolation</topic><topic>Linear algebra</topic><topic>Mathematical analysis</topic><topic>Matrices</topic><topic>Numerical analysis</topic><topic>Numerical linear algebra</topic><topic>Polynomials</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BOS, L.</creatorcontrib><creatorcontrib>DE MARCHI, S.</creatorcontrib><creatorcontrib>SOMMARIVA, A.</creatorcontrib><creatorcontrib>VIANELLO, M.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Complete</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>ProQuest Research Library</collection><collection>ProQuest Science Journals</collection><collection>Telecommunications Database</collection><collection>ProQuest Biological Science Journals</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>SIAM journal on numerical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BOS, L.</au><au>DE MARCHI, S.</au><au>SOMMARIVA, A.</au><au>VIANELLO, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA</atitle><jtitle>SIAM journal on numerical analysis</jtitle><date>2010-01-01</date><risdate>2010</risdate><volume>48</volume><issue>5</issue><spage>1984</spage><epage>1999</epage><pages>1984-1999</pages><issn>0036-1429</issn><eissn>1095-7170</eissn><abstract>We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/090779024</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0036-1429 |
| ispartof | SIAM journal on numerical analysis, 2010-01, Vol.48 (5), p.1984-1999 |
| issn | 0036-1429 1095-7170 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_901712871 |
| source | SIAM Journals Online; JSTOR Mathematics & Statistics; JSTOR |
| subjects | Algorithms Approximation Asymptotic methods Asymptotic properties Cardinality Computer programs Determinants Factorization Greedy algorithms Interpolation Linear algebra Mathematical analysis Matrices Numerical analysis Numerical linear algebra Polynomials Studies |
| title | COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T22%3A28%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=COMPUTING%20MULTIVARIATE%20FEKETE%20AND%20LEJA%20POINTS%20BY%20NUMERICAL%20LINEAR%20ALGEBRA&rft.jtitle=SIAM%20journal%20on%20numerical%20analysis&rft.au=BOS,%20L.&rft.date=2010-01-01&rft.volume=48&rft.issue=5&rft.spage=1984&rft.epage=1999&rft.pages=1984-1999&rft.issn=0036-1429&rft.eissn=1095-7170&rft_id=info:doi/10.1137/090779024&rft_dat=%3Cjstor_proqu%3E41149034%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=879723390&rft_id=info:pmid/&rft_jstor_id=41149034&rfr_iscdi=true |