On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains
The aim of this paper is to investigate, in a bounded domain of R 3 , two blending sums of univariate and bivariate C 1 quadratic spline quasi-interpolants. The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not en...
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| Veröffentlicht in: | Computer aided geometric design 2011-02, Vol.28 (2), p.89-101 |
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| creator | Remogna, S. Sablonnière, P. |
| description | The aim of this paper is to investigate, in a bounded domain of
R
3
, two blending sums of univariate and bivariate
C
1
quadratic spline quasi-interpolants.
The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not entirely inside the domain. In their definition, these functionals involve data points lying inside or on the boundary of the domain. Moreover, the weights of these functionals must be chosen so that the quasi-interpolants have the best approximation order and a reasonable infinite norm.
We give their explicit constructions, infinite norms and error estimates. In order to illustrate the approximation properties of the proposed quasi-interpolants, some numerical examples are presented and compared with those obtained by some other trivariate quasi-interpolants given recently in the literature.
► Spline approximation. ► Quasi-interpolation operator. ► Trivariate splines. |
| doi_str_mv | 10.1016/j.cagd.2010.12.002 |
| format | Article |
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R
3
, two blending sums of univariate and bivariate
C
1
quadratic spline quasi-interpolants.
The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not entirely inside the domain. In their definition, these functionals involve data points lying inside or on the boundary of the domain. Moreover, the weights of these functionals must be chosen so that the quasi-interpolants have the best approximation order and a reasonable infinite norm.
We give their explicit constructions, infinite norms and error estimates. In order to illustrate the approximation properties of the proposed quasi-interpolants, some numerical examples are presented and compared with those obtained by some other trivariate quasi-interpolants given recently in the literature.
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R
3
, two blending sums of univariate and bivariate
C
1
quadratic spline quasi-interpolants.
The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not entirely inside the domain. In their definition, these functionals involve data points lying inside or on the boundary of the domain. Moreover, the weights of these functionals must be chosen so that the quasi-interpolants have the best approximation order and a reasonable infinite norm.
We give their explicit constructions, infinite norms and error estimates. In order to illustrate the approximation properties of the proposed quasi-interpolants, some numerical examples are presented and compared with those obtained by some other trivariate quasi-interpolants given recently in the literature.
► Spline approximation. ► Quasi-interpolation operator. ► Trivariate splines.</description><subject>Applied sciences</subject><subject>Approximation</subject><subject>Blending</subject><subject>Boundaries</subject><subject>Computer aided design</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Functionals</subject><subject>Generators</subject><subject>Mathematical analysis</subject><subject>Mechanical engineering. Machine design</subject><subject>Norms</subject><subject>Quasi-interpolation operator</subject><subject>Software</subject><subject>Spline approximation</subject><subject>Splines</subject><subject>Trivariate splines</subject><issn>0167-8396</issn><issn>1879-2332</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEQx4MoWKtfwFMu4mlrHu0mC16k-IJCL3oOeUxKyjbbJrsFv72pLT16Gmbm95_HH6F7SiaU0PppPbF65SaMHApsQgi7QCMqRVMxztklGhVIVJI39TW6yXlNCkGbeoTiMuI-hb1OQfeATQvRhbjCedhk3Hk8xHNPR4fNOdsN2iXdB4vztg3xr5BDFWIPadu1OvZFH7HphujAYddtdIj5Fl153Wa4O8Ux-n57_Zp_VIvl--f8ZVHZKan7SgCphWYcvCXUlK-8Ec4LLoUlgk-19zMCdtYYzRvujJQ1SDKVxjYzZpygfIwej3O3qdsNkHu1CdlCW-6CbshK1nRWS8ZIIdmRtKnLOYFX2xQ2Ov0oStTBW7VWB2_VwVtFmSrOFdHDabzOVrc-6WhDPisZl1TKZlq45yMH5dd9gKSyDRAtuJDA9sp14b81v_HlkaA</recordid><startdate>20110201</startdate><enddate>20110201</enddate><creator>Remogna, S.</creator><creator>Sablonnière, P.</creator><general>Elsevier B.V</general><general>Elsevier</general><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>20110201</creationdate><title>On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains</title><author>Remogna, S. ; Sablonnière, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c406t-7e067a23efc01b201fb7df7387c0734aff50ec59ba393db886e8048bc952bd713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Applied sciences</topic><topic>Approximation</topic><topic>Blending</topic><topic>Boundaries</topic><topic>Computer aided design</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Functionals</topic><topic>Generators</topic><topic>Mathematical analysis</topic><topic>Mechanical engineering. Machine design</topic><topic>Norms</topic><topic>Quasi-interpolation operator</topic><topic>Software</topic><topic>Spline approximation</topic><topic>Splines</topic><topic>Trivariate splines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Remogna, S.</creatorcontrib><creatorcontrib>Sablonnière, P.</creatorcontrib><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>Computer aided geometric design</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Remogna, S.</au><au>Sablonnière, P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains</atitle><jtitle>Computer aided geometric design</jtitle><date>2011-02-01</date><risdate>2011</risdate><volume>28</volume><issue>2</issue><spage>89</spage><epage>101</epage><pages>89-101</pages><issn>0167-8396</issn><eissn>1879-2332</eissn><coden>CAGDEX</coden><abstract>The aim of this paper is to investigate, in a bounded domain of
R
3
, two blending sums of univariate and bivariate
C
1
quadratic spline quasi-interpolants.
The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not entirely inside the domain. In their definition, these functionals involve data points lying inside or on the boundary of the domain. Moreover, the weights of these functionals must be chosen so that the quasi-interpolants have the best approximation order and a reasonable infinite norm.
We give their explicit constructions, infinite norms and error estimates. In order to illustrate the approximation properties of the proposed quasi-interpolants, some numerical examples are presented and compared with those obtained by some other trivariate quasi-interpolants given recently in the literature.
► Spline approximation. ► Quasi-interpolation operator. ► Trivariate splines.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cagd.2010.12.002</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0167-8396 |
| ispartof | Computer aided geometric design, 2011-02, Vol.28 (2), p.89-101 |
| issn | 0167-8396 1879-2332 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_861568220 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | Applied sciences Approximation Blending Boundaries Computer aided design Computer science control theory systems Exact sciences and technology Functionals Generators Mathematical analysis Mechanical engineering. Machine design Norms Quasi-interpolation operator Software Spline approximation Splines Trivariate splines |
| title | On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains |
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