Analysis of Numerical Measure and Numerical Integration Based on Measure

We present a convergence analysis for a general numerical method to estimate measure function. By combining Lagrange interpolation, we propose a specific method for approximating the measure function and analyze the convergence order. Further, we analyze the error bound of numerical measure integrat...

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Main Authors:	Yinkun Wang, Jianshu Luo, Xiangling Chen
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2013/474089

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record_format	Article
spelling	doaj-1d14509436e84a47a9bff71bb58650392020-11-25T01:03:39ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/474089474089Analysis of Numerical Measure and Numerical Integration Based on MeasureYinkun Wang0Jianshu Luo1Xiangling Chen2Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics and System Science, National University of Defense Technology, Changsha 410073, ChinaCollege of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, ChinaWe present a convergence analysis for a general numerical method to estimate measure function. By combining Lagrange interpolation, we propose a specific method for approximating the measure function and analyze the convergence order. Further, we analyze the error bound of numerical measure integration and prove that the numerical measure integration can decrease the singularity for singular integrals. Numerical examples are presented to confirm the theoretical results.http://dx.doi.org/10.1155/2013/474089
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yinkun Wang Jianshu Luo Xiangling Chen
spellingShingle	Yinkun Wang Jianshu Luo Xiangling Chen Analysis of Numerical Measure and Numerical Integration Based on Measure Abstract and Applied Analysis
author_facet	Yinkun Wang Jianshu Luo Xiangling Chen
author_sort	Yinkun Wang
title	Analysis of Numerical Measure and Numerical Integration Based on Measure
title_short	Analysis of Numerical Measure and Numerical Integration Based on Measure
title_full	Analysis of Numerical Measure and Numerical Integration Based on Measure
title_fullStr	Analysis of Numerical Measure and Numerical Integration Based on Measure
title_full_unstemmed	Analysis of Numerical Measure and Numerical Integration Based on Measure
title_sort	analysis of numerical measure and numerical integration based on measure
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2013-01-01
description	We present a convergence analysis for a general numerical method to estimate measure function. By combining Lagrange interpolation, we propose a specific method for approximating the measure function and analyze the convergence order. Further, we analyze the error bound of numerical measure integration and prove that the numerical measure integration can decrease the singularity for singular integrals. Numerical examples are presented to confirm the theoretical results.
url	http://dx.doi.org/10.1155/2013/474089
work_keys_str_mv	AT yinkunwang analysisofnumericalmeasureandnumericalintegrationbasedonmeasure AT jianshuluo analysisofnumericalmeasureandnumericalintegrationbasedonmeasure AT xianglingchen analysisofnumericalmeasureandnumericalintegrationbasedonmeasure
_version_	1725200062288494592

Analysis of Numerical Measure and Numerical Integration Based on Measure

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