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Volume 27, Issue 6
Hermite Scattered Data Fitting by the Penalized Least Squares Method

Tianhe Zhou & Danfu Han

DOI: 10.4208//jcm.2009.09-m2540

J. Comp. Math., 27 (2009), pp. 802-811.

Published online: 2009-12

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  • Abstract

Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker [Serdica, 18 (2002), pp.1001-1020] to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bound for the extension method. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.  

  • Keywords

Bivariate splines, Scattered data fitting, Extension of penalized least squares method.

  • AMS Subject Headings

41A15, 65M60, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-802, author = {Tianhe Zhou and Danfu Han}, title = {Hermite Scattered Data Fitting by the Penalized Least Squares Method}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {6}, pages = {802--811}, abstract = {

Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker [Serdica, 18 (2002), pp.1001-1020] to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bound for the extension method. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.  

}, issn = {1991-7139}, doi = {https://doi.org/10.4208//jcm.2009.09-m2540}, url = {http://global-sci.org/intro/article_detail/jcm/8604.html} }
TY - JOUR T1 - Hermite Scattered Data Fitting by the Penalized Least Squares Method AU - Tianhe Zhou & Danfu Han JO - Journal of Computational Mathematics VL - 6 SP - 802 EP - 811 PY - 2009 DA - 2009/12 SN - 27 DO - http://doi.org/10.4208//jcm.2009.09-m2540 UR - https://global-sci.org/intro/article_detail/jcm/8604.html KW - Bivariate splines, Scattered data fitting, Extension of penalized least squares method. AB -

Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker [Serdica, 18 (2002), pp.1001-1020] to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bound for the extension method. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.  

Tianhe Zhou and Danfu Han. (2009). Hermite Scattered Data Fitting by the Penalized Least Squares Method. Journal of Computational Mathematics. 27 (6). 802-811. doi:10.4208//jcm.2009.09-m2540
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