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

Moment vector equations (MVEs) are presented for use in approximating and analyzing multi-dimensional non-linear discreteand 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. key words: approximation, linearization, non-linear, statistics