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Automatic computation of hierarchical biquadratic smoothing slines with minimum GCV

Hancock, P A; Hutchinson, Michael

Description

A computationally efficient numerical strategy for fitting approximate minimum GCV bivariate thin plate smoothing splines to large noisy data sets was developed. The procedure discretises the bivariate thin plate smoothing spline equations using biquadratic B-splines and uses a nested grid SOR iterative strategy to solve the discretised system. For efficient optimisation, the process incorporates a double iteration that simultaneously updates both the discretised solution and the estimate of...[Show more]

dc.contributor.authorHancock, P A
dc.contributor.authorHutchinson, Michael
dc.date.accessioned2015-12-07T22:38:28Z
dc.identifier.issn0098-3004
dc.identifier.urihttp://hdl.handle.net/1885/23463
dc.description.abstractA computationally efficient numerical strategy for fitting approximate minimum GCV bivariate thin plate smoothing splines to large noisy data sets was developed. The procedure discretises the bivariate thin plate smoothing spline equations using biquadratic B-splines and uses a nested grid SOR iterative strategy to solve the discretised system. For efficient optimisation, the process incorporates a double iteration that simultaneously updates both the discretised solution and the estimate of the minimum GCV smoothing parameter. The GCV was estimated using a minimum variance stochastic estimator of the trace of the influence matrix associated with the fitted spline surface. A Taylor series expansion was used to estimate the smoothing parameter that minimises the GCV estimate. The computational cost of the procedure is optimal in the sense that it is proportional to the number of grid points supporting the fitted biquadratic spline. Convergence was improved by adding a first order correction to the solution estimate after each smoothing parameter update. The algorithm was tested on several simulated data sets with varying spatial complexity and noise level. An accurate approximation to the analytic minimum GCV thin plate smoothing spline was obtained in all cases.
dc.publisherPergamon Press
dc.sourceComputers and Geosciences
dc.subjectKeywords: Algorithms; Approximation theory; Convergence of numerical methods; Finite element method; Iterative methods; Matrix algebra; Optimization; Random processes; Generalised cross validation; Multilevel method; Randomized trace; Smoothing spline; Computationa Finite element; Generalised cross validation; Multilevel method; Randomized trace; Smoothing spline
dc.titleAutomatic computation of hierarchical biquadratic smoothing slines with minimum GCV
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume32
dc.date.issued2006
local.identifier.absfor040699 - Physical Geography and Environmental Geoscience not elsewhere classified
local.identifier.ariespublicationU3923986xPUB27
local.type.statusPublished Version
local.contributor.affiliationHancock, P A, Imperial College London
local.contributor.affiliationHutchinson, Michael, College of Medicine, Biology and Environment, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage834
local.bibliographicCitation.lastpage845
local.identifier.doi10.1016/j.cageo.2005.10.010
dc.date.updated2015-12-07T10:38:33Z
local.identifier.scopusID2-s2.0-33744986298
CollectionsANU Research Publications

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