An Improved Moving Least Squares Method for Curve and Surface Fitting
The moving least squares (MLS) method has been developed for the fitting of measured data contaminated with random error. The local approximants of MLS method only take the error of dependent variable into account, whereas the independent variable of measured data always contains random error. Consi...
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| Veröffentlicht in: | Mathematical problems in engineering 2013-01, Vol.2013 (2013), p.1-6 |
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| container_title | Mathematical problems in engineering |
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| creator | Hu, Ming Ji, Shijun Zhao, Ji Gu, Tianqi Zhang, Lei Li, Xiangbo |
| description | The moving least squares (MLS) method has been developed for the fitting of measured data contaminated with random error. The local approximants of MLS method only take the error of dependent variable into account, whereas the independent variable of measured data always contains random error. Considering the errors of all variables, this paper presents an improved moving least squares (IMLS) method to generate curve and surface for the measured data. In IMLS method, total least squares (TLS) with a parameter λ based on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameter λ. Numerical examples for curve and surface fitting are given to prove the performance of IMLS method. |
| doi_str_mv | 10.1155/2013/159694 |
| format | Article |
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The local approximants of MLS method only take the error of dependent variable into account, whereas the independent variable of measured data always contains random error. Considering the errors of all variables, this paper presents an improved moving least squares (IMLS) method to generate curve and surface for the measured data. In IMLS method, total least squares (TLS) with a parameter λ based on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameter λ. Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2013/159694</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Advanced manufacturing technologies ; Algorithms ; Approximants ; Computational mathematics ; Curve fitting ; Dependent variables ; Economic models ; Error analysis ; Errors ; Fittings ; Independent variables ; Least squares method ; Mathematical analysis ; Mathematical models ; Mathematical problems ; Metal forming ; Methods ; Principal components analysis ; Random errors ; Singular value decomposition</subject><ispartof>Mathematical problems in engineering, 2013-01, Vol.2013 (2013), p.1-6</ispartof><rights>Copyright © 2013 Lei Zhang et al.</rights><rights>Copyright © 2013 Lei Zhang et al.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c389t-c101bbc53d775d71ffa9e8c18679cccf94bdb2a527643212709c9ffac9a32b693</citedby><cites>FETCH-LOGICAL-c389t-c101bbc53d775d71ffa9e8c18679cccf94bdb2a527643212709c9ffac9a32b693</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><contributor>Andrianov, Igor</contributor><creatorcontrib>Hu, Ming</creatorcontrib><creatorcontrib>Ji, Shijun</creatorcontrib><creatorcontrib>Zhao, Ji</creatorcontrib><creatorcontrib>Gu, Tianqi</creatorcontrib><creatorcontrib>Zhang, Lei</creatorcontrib><creatorcontrib>Li, Xiangbo</creatorcontrib><title>An Improved Moving Least Squares Method for Curve and Surface Fitting</title><title>Mathematical problems in engineering</title><description>The moving least squares (MLS) method has been developed for the fitting of measured data contaminated with random error. 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Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.</description><subject>Advanced manufacturing technologies</subject><subject>Algorithms</subject><subject>Approximants</subject><subject>Computational mathematics</subject><subject>Curve fitting</subject><subject>Dependent variables</subject><subject>Economic models</subject><subject>Error analysis</subject><subject>Errors</subject><subject>Fittings</subject><subject>Independent variables</subject><subject>Least squares method</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical problems</subject><subject>Metal forming</subject><subject>Methods</subject><subject>Principal components analysis</subject><subject>Random errors</subject><subject>Singular value decomposition</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>BENPR</sourceid><recordid>eNqF0MFLwzAUBvAiCs7pybsEvIhSl5c0SXMcY9PBhocpeAtpmmhla7eknfjfm1EP4sXTe4ffe3x8SXIJ-B6AsRHBQEfAJJfZUTIAxmnKIBPHccckS4HQ19PkLIQPjAkwyAfJdFyj-Wbrm70t0bLZV_UbWlgdWrTaddrbgJa2fW9K5BqPJp3fW6TrEq0677SxaFa1bTw5T06cXgd78TOHycts-jx5TBdPD_PJeJEamss2NYChKAyjpRCsFOCcljY3kHMhjTFOZkVZEM2I4BklQASWRkZkpKak4JIOk5v-bwy862xo1aYKxq7XurZNFxRwAUwAyVik13_oR9P5OqZTIHMOgmNMo7rrlfFNCN46tfXVRvsvBVgdKlWHSlVfadS3vX6v6lJ_Vv_gqx7bSKzTvzDOGWf0GybffZk</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>Hu, Ming</creator><creator>Ji, Shijun</creator><creator>Zhao, Ji</creator><creator>Gu, Tianqi</creator><creator>Zhang, Lei</creator><creator>Li, Xiangbo</creator><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20130101</creationdate><title>An Improved Moving Least Squares Method for Curve and Surface Fitting</title><author>Hu, Ming ; Ji, Shijun ; Zhao, Ji ; Gu, Tianqi ; Zhang, Lei ; Li, Xiangbo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c389t-c101bbc53d775d71ffa9e8c18679cccf94bdb2a527643212709c9ffac9a32b693</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Advanced manufacturing technologies</topic><topic>Algorithms</topic><topic>Approximants</topic><topic>Computational mathematics</topic><topic>Curve fitting</topic><topic>Dependent variables</topic><topic>Economic models</topic><topic>Error analysis</topic><topic>Errors</topic><topic>Fittings</topic><topic>Independent variables</topic><topic>Least squares method</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematical problems</topic><topic>Metal forming</topic><topic>Methods</topic><topic>Principal components analysis</topic><topic>Random errors</topic><topic>Singular value decomposition</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Ming</creatorcontrib><creatorcontrib>Ji, Shijun</creatorcontrib><creatorcontrib>Zhao, Ji</creatorcontrib><creatorcontrib>Gu, Tianqi</creatorcontrib><creatorcontrib>Zhang, Lei</creatorcontrib><creatorcontrib>Li, Xiangbo</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</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>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</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><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Ming</au><au>Ji, Shijun</au><au>Zhao, Ji</au><au>Gu, Tianqi</au><au>Zhang, Lei</au><au>Li, Xiangbo</au><au>Andrianov, Igor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Improved Moving Least Squares Method for Curve and Surface Fitting</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2013-01-01</date><risdate>2013</risdate><volume>2013</volume><issue>2013</issue><spage>1</spage><epage>6</epage><pages>1-6</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>The moving least squares (MLS) method has been developed for the fitting of measured data contaminated with random error. The local approximants of MLS method only take the error of dependent variable into account, whereas the independent variable of measured data always contains random error. Considering the errors of all variables, this paper presents an improved moving least squares (IMLS) method to generate curve and surface for the measured data. In IMLS method, total least squares (TLS) with a parameter λ based on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameter λ. Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2013/159694</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| source | Wiley Online Library Open Access; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | Advanced manufacturing technologies Algorithms Approximants Computational mathematics Curve fitting Dependent variables Economic models Error analysis Errors Fittings Independent variables Least squares method Mathematical analysis Mathematical models Mathematical problems Metal forming Methods Principal components analysis Random errors Singular value decomposition |
| title | An Improved Moving Least Squares Method for Curve and Surface Fitting |
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