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

Hideki SATOH

doi:10.1093/ietfec/e89-a.1.270

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

Hideki SATOH

Full Text Views

0

Share
Cite this

Summary :

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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.1 pp.270-279

Publication Date: 2006/01/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.1.270

Type of Manuscript: PAPER

Category: Nonlinear Problems

Cite this

Copy

Hideki SATOH, "Approximation and Analysis of Non-linear Equations in a Moment Vector Space" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 1, pp. 270-279, January 2006, doi: 10.1093/ietfec/e89-a.1.270.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.1.270/_p

Copy

@ARTICLE{e89-a_1_270,
author={Hideki SATOH, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Approximation and Analysis of Non-linear Equations in a Moment Vector Space},
year={2006},
volume={E89-A},
number={1},
pages={270-279},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e89-a.1.270},
ISSN={1745-1337},
month={January},}

Copy

TY - JOUR
TI - Approximation and Analysis of Non-linear Equations in a Moment Vector Space
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 270
EP - 279
AU - Hideki SATOH
PY - 2006
DO - 10.1093/ietfec/e89-a.1.270
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2006
AB - 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.
ER -