Algorithms for DEDICOM: acceleration, deceleration, or neither?

Takane's original algorithm for DEDICOM (DEcomposition into DIrectional COMponents) was proposed more than two decades ago. There have been a couple of significant developments since then: Kiers et al.'s modification to ensure monotonic convergence of the algorithm, and Jennrich's rec...

Full description

Saved in:
Bibliographic Details
Published in:Journal of chemometrics 2009-07, Vol.23 (7-8), p.364-370
Main Authors: Takane, Yoshio, Zhang, Zhidong
Format: Article
Language:English
Subjects:
Algorithms
Chemistry
Convergence
Deceleration
Eigenvalues
Exact sciences and technology
Extrapolation
General and physical chemistry
General. Nomenclature, chemical documentation, computer chemistry
Mathematical analysis
Matrix
minimal polynomial extrapolation
Modifications
simultaneous power method
Takane's algorithm for DEDICOM
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
Vectors (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Takane's original algorithm for DEDICOM (DEcomposition into DIrectional COMponents) was proposed more than two decades ago. There have been a couple of significant developments since then: Kiers et al.'s modification to ensure monotonic convergence of the algorithm, and Jennrich's recommendation to use the modified algorithm only when Takane's original algorithm violates the monotonicity. In this paper, we argue that neither of these modifications is essential, drawing a close relationship between Takane's algorithm and the simultaneous power method for obtaining dominant eigenvalues and vectors of a symmetric matrix. By ignoring monotonicity, we can develop a much more efficient algorithm by simple modifications of Takane's original algorithm, as demonstrated in this paper. More specifically, we incorporate the minimum polynomial extrapolation (MPE) method to accelerate the convergence of Takane's algorithm, and show that it significantly cuts down the computation time. Copyright © 2009 John Wiley & Sons, Ltd. DEDICOM is a model for the analysis of square asymmetric tables. The speed of convergence in Takane's original algorithm for DEDICOM was substantially improved by incorporating the minimal polynomial extraporation (MPE) method. The efficiency of the new algorithm was demonstrated by numerical examples.
ISSN:0886-9383
1099-128X
1099-128X
DOI:10.1002/cem.1230