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Mathematical Problems in Engineering
Volume 2013, Article ID 159694, 6 pages
Research Article

An Improved Moving Least Squares Method for Curve and Surface Fitting

College of Mechanical Science and Engineering, Nanling Campus, Jilin University, Changchun 130025, China

Received 22 August 2013; Revised 1 November 2013; Accepted 1 November 2013

Academic Editor: Igor Andrianov

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.


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 based on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameter . Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.