Fast generalized cross validation using Krylov subspace methods

Sidje, Roger B., Williams, Alan B. and Burrage, Kevin (2008) Fast generalized cross validation using Krylov subspace methods. Numerical Algorithms, 47 2: 109-131. doi:10.1007/s11075-007-9150-y


Author Sidje, Roger B.
Williams, Alan B.
Burrage, Kevin
Title Fast generalized cross validation using Krylov subspace methods
Journal name Numerical Algorithms   Check publisher's open access policy
ISSN 1017-1398
Publication date 2008-02
Sub-type Article (original research)
DOI 10.1007/s11075-007-9150-y
Volume 47
Issue 2
Start page 109
End page 131
Total pages 23
Place of publication Basel, Switzerland
Publisher J.C. Baltzer
Language eng
Subject 0102 Applied Mathematics
Formatted abstract
The task of fitting smoothing spline surfaces to meteorological data such as temperature or rainfall observations is computationally intensive. The generalized cross validation (GCV) smoothing algorithm, if implemented using direct matrix techniques, is O(n 3) computationally, and memory requirements are O(n 2). Thus, for data sets larger than a few hundred observations, the algorithm is prohibitively slow. The core of the algorithm consists of solving series of shifted linear systems, and iterative techniques have been used to lower the computational complexity and facilitate implementation on a variety of supercomputer architectures. For large data sets though, the execution time is still quite high. In this paper we describe a Lanczos based approach that avoids explicitly solving the linear systems and dramatically reduces the amount of time required to fit surfaces to sets of data.
Keyword Lanczos
Linear systems
Generalized cross validation
Q-Index Code C1
Q-Index Status Provisional Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
Institute for Molecular Bioscience - Publications
 
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Created: Thu, 03 Sep 2009, 10:25:52 EST by Mr Andrew Martlew on behalf of Institute for Molecular Bioscience