An Improved Moving Least Squares Method for Curve and Surface Fitting

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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math>based on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math>. Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.