Optimal smoothing and interpolating splines with constraints
This paper considers the problem for designing optimal smoothing and interpolating splines with equality and/or inequality constraints. The splines are constituted by employing normalized uniform B-splines as the basis functions, namely as weighted sum of shifted B-splines of degree k. Then a centra...
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| Veröffentlicht in: | Applied mathematics and computation 2011-11, Vol.218 (5), p.1831-1844 |
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| creator | Kano, Hiroyuki Fujioka, Hiroyuki Martin, Clyde F. |
| description | This paper considers the problem for designing optimal smoothing and interpolating splines with equality and/or inequality constraints. The splines are constituted by employing normalized uniform B-splines as the basis functions, namely as weighted sum of shifted B-splines of degree
k. Then a central issue is to determine an optimal vector of the so-called control points. By employing such an approach, it is shown that various types of constraints are formulated as linear function of the control points, and the problems reduce to quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples including approximation of probability density functions, approximation of discontinuous functions, and trajectory planning. |
| doi_str_mv | 10.1016/j.amc.2011.06.067 |
| format | Article |
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k. Then a central issue is to determine an optimal vector of the so-called control points. By employing such an approach, it is shown that various types of constraints are formulated as linear function of the control points, and the problems reduce to quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples including approximation of probability density functions, approximation of discontinuous functions, and trajectory planning.</description><subject>Approximation</subject><subject>B-splines</subject><subject>Equality/inequality constraint</subject><subject>Inequalities</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Optimal interpolating splines</subject><subject>Optimal smoothing splines</subject><subject>Optimization</subject><subject>Quadratic programming</subject><subject>Smoothing</subject><subject>Splines</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAUxIMouK5-AG-9eWp9adpki15k8R8s7EXPIU1f3CxtU5Os4rc3Sz0LAwOP3zyYIeSaQkGB8tt9oQZdlEBpATxJnJAFXQmW17xqTskCoOE5A2Dn5CKEPQAITqsFud9O0Q6qz8LgXNzZ8SNTY5fZMaKfXK_i8RKm3o4Ysm8bd5l2Y4heJSJckjOj-oBXf74k70-Pb-uXfLN9fl0_bHLNyibmpqZC1ww62jarlW4FZ5yDplAzxVqg2CnkQghQ2oBpjTBQ1pXGuuqYEGXLluRm_jt593nAEOVgg8a-VyO6Q5BNycsGmgoSSWdSexeCRyMnn-r5H0lBHoeSe5mGksehJPAkkTJ3cwZThS-LXgZtcdTYWY86ys7Zf9K_oOtxCw</recordid><startdate>20111101</startdate><enddate>20111101</enddate><creator>Kano, Hiroyuki</creator><creator>Fujioka, Hiroyuki</creator><creator>Martin, Clyde F.</creator><general>Elsevier Inc</general><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>20111101</creationdate><title>Optimal smoothing and interpolating splines with constraints</title><author>Kano, Hiroyuki ; Fujioka, Hiroyuki ; Martin, Clyde F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c329t-f517c530d1b988cb763660c1053a3b01edae67770acf0fbf7f0254ce54d3772b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Approximation</topic><topic>B-splines</topic><topic>Equality/inequality constraint</topic><topic>Inequalities</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Optimal interpolating splines</topic><topic>Optimal smoothing splines</topic><topic>Optimization</topic><topic>Quadratic programming</topic><topic>Smoothing</topic><topic>Splines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kano, Hiroyuki</creatorcontrib><creatorcontrib>Fujioka, Hiroyuki</creatorcontrib><creatorcontrib>Martin, Clyde F.</creatorcontrib><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>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kano, Hiroyuki</au><au>Fujioka, Hiroyuki</au><au>Martin, Clyde F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal smoothing and interpolating splines with constraints</atitle><jtitle>Applied mathematics and computation</jtitle><date>2011-11-01</date><risdate>2011</risdate><volume>218</volume><issue>5</issue><spage>1831</spage><epage>1844</epage><pages>1831-1844</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><abstract>This paper considers the problem for designing optimal smoothing and interpolating splines with equality and/or inequality constraints. The splines are constituted by employing normalized uniform B-splines as the basis functions, namely as weighted sum of shifted B-splines of degree
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| ispartof | Applied mathematics and computation, 2011-11, Vol.218 (5), p.1831-1844 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Approximation B-splines Equality/inequality constraint Inequalities Mathematical analysis Mathematical models Optimal interpolating splines Optimal smoothing splines Optimization Quadratic programming Smoothing Splines |
| title | Optimal smoothing and interpolating splines with constraints |
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