A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain
In the paper [H.S. Kim, Y.J. Ahn, Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain, J. Comput. Appl. Math. 216 (2008) 14–19], Kim and Ahn proved that the best constrained degree reduction of a polynomial over d -dimensional simplex domain in L 2 -norm equals t...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2009-07, Vol.229 (1), p.324-326 |
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| creator | Lu, Lizheng |
| description | In the paper [H.S. Kim, Y.J. Ahn, Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain, J. Comput. Appl. Math. 216 (2008) 14–19], Kim and Ahn proved that the best constrained degree reduction of a polynomial over
d
-dimensional simplex domain in
L
2
-norm equals the best approximation of weighted Euclidean norm of the Bernstein–Bézier coefficients of the given polynomial. In this paper, we presented a counterexample to show that the approximating polynomial of lower degree to a polynomial is virtually non-existent when
d
≥
2
. Furthermore, we provide an assumption to guarantee the existence of solution for the constrained degree reduction. |
| doi_str_mv | 10.1016/j.cam.2008.10.032 |
| format | Article |
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d
-dimensional simplex domain in
L
2
-norm equals the best approximation of weighted Euclidean norm of the Bernstein–Bézier coefficients of the given polynomial. In this paper, we presented a counterexample to show that the approximating polynomial of lower degree to a polynomial is virtually non-existent when
d
≥
2
. Furthermore, we provide an assumption to guarantee the existence of solution for the constrained degree reduction.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2008.10.032</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Bernstein polynomials ; Constrained degree reduction ; Degree elevation ; Exact sciences and technology ; Mathematical analysis ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Sciences and techniques of general use ; Simplex domain</subject><ispartof>Journal of computational and applied mathematics, 2009-07, Vol.229 (1), p.324-326</ispartof><rights>2008 Elsevier B.V.</rights><rights>2009 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c433t-9fa6f43501e9ecf0068eed3c127b1f6202ecfb54673b2bf99b502a5f995fb003</citedby><cites>FETCH-LOGICAL-c433t-9fa6f43501e9ecf0068eed3c127b1f6202ecfb54673b2bf99b502a5f995fb003</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cam.2008.10.032$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21544816$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Lu, Lizheng</creatorcontrib><title>A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain</title><title>Journal of computational and applied mathematics</title><description>In the paper [H.S. Kim, Y.J. Ahn, Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain, J. Comput. Appl. Math. 216 (2008) 14–19], Kim and Ahn proved that the best constrained degree reduction of a polynomial over
d
-dimensional simplex domain in
L
2
-norm equals the best approximation of weighted Euclidean norm of the Bernstein–Bézier coefficients of the given polynomial. In this paper, we presented a counterexample to show that the approximating polynomial of lower degree to a polynomial is virtually non-existent when
d
≥
2
. Furthermore, we provide an assumption to guarantee the existence of solution for the constrained degree reduction.</description><subject>Bernstein polynomials</subject><subject>Constrained degree reduction</subject><subject>Degree elevation</subject><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Sciences and techniques of general use</subject><subject>Simplex domain</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9kE1uFDEQRi0EEkPgAOy8Iax6Uv5pu1uskogkSJGyyd5yu8vIo257sHuiJKvcgVNwDm7CSeLRRCyzcrn86ivrEfKZwZoBUyebtbPzmgN09b4Gwd-QFet03zCtu7dkBULrBiTX78mHUjYAoHomVwRPaUwL0hSpS7Es2YaIIx3xZ0akGcedW0J9TJ5u0_QQ0xzsVGiI9Axz5THEf0-_z_7-eQyYqU95pumuViXM2wnv6ZjmmviRvPN1DD-9nEfk9uL77flVc31z-eP89LpxUoil6b1VXooWGPbofP1jhzgKx7gemFcceO0OrVRaDHzwfT-0wG1bi9YPAOKIfD3EbnP6tcOymDkUh9NkI6ZdMT0IJaQGWcnjV0khpVJMiAqyA-hyKiWjN9scZpsfDAOzN282ppo3e_P7VjVfZ768hNvi7OSzjS6U_4OctVJ2TFXu24HDquSu-jPFBYwOx5DRLWZM4ZUtzx29mzk</recordid><startdate>20090701</startdate><enddate>20090701</enddate><creator>Lu, Lizheng</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20090701</creationdate><title>A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain</title><author>Lu, Lizheng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c433t-9fa6f43501e9ecf0068eed3c127b1f6202ecfb54673b2bf99b502a5f995fb003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Bernstein polynomials</topic><topic>Constrained degree reduction</topic><topic>Degree elevation</topic><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Sciences and techniques of general use</topic><topic>Simplex domain</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lu, Lizheng</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lu, Lizheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2009-07-01</date><risdate>2009</risdate><volume>229</volume><issue>1</issue><spage>324</spage><epage>326</epage><pages>324-326</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>In the paper [H.S. Kim, Y.J. Ahn, Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain, J. Comput. Appl. Math. 216 (2008) 14–19], Kim and Ahn proved that the best constrained degree reduction of a polynomial over
d
-dimensional simplex domain in
L
2
-norm equals the best approximation of weighted Euclidean norm of the Bernstein–Bézier coefficients of the given polynomial. In this paper, we presented a counterexample to show that the approximating polynomial of lower degree to a polynomial is virtually non-existent when
d
≥
2
. Furthermore, we provide an assumption to guarantee the existence of solution for the constrained degree reduction.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2008.10.032</doi><tpages>3</tpages><oa>free_for_read</oa></addata></record> |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Access via ScienceDirect (Elsevier) |
| subjects | Bernstein polynomials Constrained degree reduction Degree elevation Exact sciences and technology Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Sciences and techniques of general use Simplex domain |
| title | A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain |
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