Summary
We present an iterative algorithm for computing an approximation to data in wells using the norm function in three dimensions augmented with a tensor product of two dimensional Lagrange functions with one dimensional linear inter- polants. This augmentation can be thought of as a trend. The algorithm avoids the stability problems associated with data which have very different separation in dif- ferent directions. In this case, data are close in the vertical direction inside each well, but the wells are relatively far apart. We will give an estimate of the convergence rate of the algorithm in terms of the vertical point spacing and the horizontal well separation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R.K. Beatson and G.N. Newsam: Fast evaluation of radial basis functions: I. Computers & Mathematics with Applications 24, 1992, 7–19.
R.K. Beatson and G.N. Newsam: Fast evaluation of radial basis functions: moment-based methods. SIAM Journal on Scientific Computing 19, 1998, 1428–1449.
A.C. Faul and M.J.D. Powell: Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions. Advances in Computational Mathematics 11, 1999, 183–192.
L. Greengard and V. Rokhlin: A fast algorithm for particle simulations. Journal of Computational Physics 73, 1987, 325–348.
M.J.D. Powell: A new iterative algorithm for thin plate spline interpolation in two dimensions. Annals of Numerical Mathematics 4, 1997, 519–527.
H. Wendland: Scattered Data Approximation. Cambridge University Press, Cambridge, UK, 2005.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, B., Levesley, J. (2011). Fast and Stable Interpolation of Well Data Using the Norm Function. In: Georgoulis, E., Iske, A., Levesley, J. (eds) Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16876-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-16876-5_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16875-8
Online ISBN: 978-3-642-16876-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)