Approximation and Analysis of Non-linear Equations in a Moment Vector Space

Hideki SATOH  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.1   pp.270-279
Publication Date: 2006/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.1.270
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
approximation,  linearization,  non-linear,  statistics,  

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Moment vector equations (MVEs) are presented for use in approximating and analyzing multi-dimensional non-linear discrete- and continuous-time equations. A non-linear equation is expanded into simultaneous equations of generalized moments and then reduced to an MVE of a coefficient matrix and a moment vector. The MVE can be used to analyze the statistical properties, such as the mean, variance, covariance, and power spectrum, of the non-linear equation. Moreover, we can approximately express a combination of non-linear equations by using a combination of MVEs of the equations. Evaluation of the statistical properties of Lorenz equations and of a combination of logistic equations based on the MVE approach showed that MVEs can be used to approximate non-linear equations in statistical measurements.