A Statistical Analysis of Non-linear Equations Based on a Linear Combination of Generalized Moments

Hideki SATOH

A Statistical Analysis of Non-linear Equations Based on a Linear Combination of Generalized Moments

Hideki SATOH

Full Text Views

0

Share
Cite this

Summary :

A moment matrix analysis (MMA) method can derive macroscopic statistical properties such as moments, response time, and power spectra of non-linear equations without solving the equations. MMA expands a non-linear equation into simultaneous linear equations of moments, and reduces it to a linear equation of their coefficient matrix and a moment vector. We can analyze the statistical properties from the eigenvalues and eigenvectors of the coefficient matrix. This paper presents (1) a systematic procedure to linearize non-linear equations and (2) an expansion of the previous work of MMA to derive the statistical properties of various non-linear equations. The statistical properties of the logistic map were evaluated by using MMA and computer simulation, and it is shown that the proposed systematic procedure was effective and that MMA could accurately approximate the statistical properties of the logistic map even though such a map had strong non-linearity.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.12 pp.3381-3388

Publication Date: 2004/12/01

Publicized

Online ISSN

DOI

Type of Manuscript: PAPER

Category: Nonlinear Problems

Cite this

Copy

Hideki SATOH, "A Statistical Analysis of Non-linear Equations Based on a Linear Combination of Generalized Moments" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 12, pp. 3381-3388, December 2004, doi: .
Abstract: A moment matrix analysis (MMA) method can derive macroscopic statistical properties such as moments, response time, and power spectra of non-linear equations without solving the equations. MMA expands a non-linear equation into simultaneous linear equations of moments, and reduces it to a linear equation of their coefficient matrix and a moment vector. We can analyze the statistical properties from the eigenvalues and eigenvectors of the coefficient matrix. This paper presents (1) a systematic procedure to linearize non-linear equations and (2) an expansion of the previous work of MMA to derive the statistical properties of various non-linear equations. The statistical properties of the logistic map were evaluated by using MMA and computer simulation, and it is shown that the proposed systematic procedure was effective and that MMA could accurately approximate the statistical properties of the logistic map even though such a map had strong non-linearity.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e87-a_12_3381/_p

Copy

@ARTICLE{e87-a_12_3381,
author={Hideki SATOH, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Statistical Analysis of Non-linear Equations Based on a Linear Combination of Generalized Moments},
year={2004},
volume={E87-A},
number={12},
pages={3381-3388},
abstract={A moment matrix analysis (MMA) method can derive macroscopic statistical properties such as moments, response time, and power spectra of non-linear equations without solving the equations. MMA expands a non-linear equation into simultaneous linear equations of moments, and reduces it to a linear equation of their coefficient matrix and a moment vector. We can analyze the statistical properties from the eigenvalues and eigenvectors of the coefficient matrix. This paper presents (1) a systematic procedure to linearize non-linear equations and (2) an expansion of the previous work of MMA to derive the statistical properties of various non-linear equations. The statistical properties of the logistic map were evaluated by using MMA and computer simulation, and it is shown that the proposed systematic procedure was effective and that MMA could accurately approximate the statistical properties of the logistic map even though such a map had strong non-linearity.},
keywords={},
doi={},
ISSN={},
month={December},}

Copy

TY - JOUR
TI - A Statistical Analysis of Non-linear Equations Based on a Linear Combination of Generalized Moments
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3381
EP - 3388
AU - Hideki SATOH
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2004
AB - A moment matrix analysis (MMA) method can derive macroscopic statistical properties such as moments, response time, and power spectra of non-linear equations without solving the equations. MMA expands a non-linear equation into simultaneous linear equations of moments, and reduces it to a linear equation of their coefficient matrix and a moment vector. We can analyze the statistical properties from the eigenvalues and eigenvectors of the coefficient matrix. This paper presents (1) a systematic procedure to linearize non-linear equations and (2) an expansion of the previous work of MMA to derive the statistical properties of various non-linear equations. The statistical properties of the logistic map were evaluated by using MMA and computer simulation, and it is shown that the proposed systematic procedure was effective and that MMA could accurately approximate the statistical properties of the logistic map even though such a map had strong non-linearity.
ER -