On derivative estimation and the solution of least squares problems

Belward, J. A., Turner, I. W. and Ilic, M. (2008) On derivative estimation and the solution of least squares problems. Journal of Computational and Applied Mathematics, 222 2: 511-523. doi:10.1016/j.cam.2007.11.022

Author Belward, J. A.
Turner, I. W.
Ilic, M.
Title On derivative estimation and the solution of least squares problems
Journal name Journal of Computational and Applied Mathematics   Check publisher's open access policy
ISSN 0377-0427
Publication date 2008
Sub-type Article (original research)
DOI 10.1016/j.cam.2007.11.022
Volume 222
Issue 2
Start page 511
End page 523
Total pages 13
Editor Goovaerts, M. J.
Mitsui, T.
Monk, P.
Place of publication Netherlands
Publisher Elsevier B. V.
Collection year 2009
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010301 Numerical Analysis
010303 Optimisation
Abstract Surface interpolation finds application in many aspects of science and technology. Two specific areas of interest are surface reconstruction techniques for plant architecture and approximating cell face fluxes in the finite volume discretisation strategy for solving partial differential equations numerically. An important requirement of both applications is accurate local gradient estimation. In surface reconstruction this gradient information is used to increase the accuracy of the local interpolant, while in the finite volume framework accurate gradient information is essential to ensure second order spatial accuracy of the discretisation. In this work two different least squares strategies for approximating these local gradients are investigated and the errors associated with each analysed. It is shown that although the two strategies appear different, they produce the same least squares error. Some carefully chosen case studies are used to elucidate this finding.
Keyword Derivative estimation
Heat transfer and diffusion
Surface approximation
Plant architecture
Q-Index Code C1
Q-Index Status Confirmed Code

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Created: Tue, 10 Feb 2009, 12:18:22 EST by Marie Grove on behalf of School of Mathematics & Physics