Surface fitting using GCV smoothing splines on supercomputers

Authors:
Alan Williams;Kevin Burrage
Affiliations:
Department of Mathematics, University of Queensland, Brisbane, Australia 4072;Department of Mathematics, University of Queensland, Brisbane, Australia 4072
Venue:
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Year:
1995

Citing 3
Cited 0

The computation of generalized cross-validation functions through householder tridiagonalization with applications to the fitting of interaction spline models

SIAM Journal on Matrix Analysis and Applications
The implementation of a Generalized Cross Validation algorithm using deflation techniques for linear systems

Applied Numerical Mathematics - Special issue on massively parallel computing and applications
ADVISE - Agricultural Developmental Visualisation Interactive Software Environment

CONPAR 94 - VAPP VI Proceedings of the Third Joint International Conference on Vector and Parallel Processing: Parallel Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The task of fitting smoothing spline surfaces to meteorological data such as temperature or rainfall observations is computationally intensive. The Generalised Cross Validation (GCV) smoothing algorithm is O(n鲁) computationally, and memory requirements are 0(n虏). Fitting a spline to a moderately sized data set of, for example. 1080 observations and calculating an output surface grid of dimension 220 脳 220 involves approximately 5 billion floating point operations, and takes approximately 19 minutes of execution time on a Sun SPARC2 workstation. Since fitting a surface to data collected from the whole of Australia could conceivably involve data sets with approximately 10000 points, and because it is desirable to be able to fit surfaces of at least 1000 data points in 1 to 5 seconds for use in interactive visualisations, it is crucial to be able to take advantage of supercomputing resources. This paper describes the adaptation of the surface fitting program to different supercomputing platforms, and the results achieved.