Mathematical Demoeconomy

D. Zero-order multiplicative algorithms for positive solutions to nonlinear equations

D.1 Introduction

Consider the following forms of nonlinear equations:

(D.1)

(D.2)

Suppose that these equations possess a unique positive solution x^∗ > 0. The symbol ⊗ designates componentwise product.

There exists no fundamental difference between the first and second forms of equations. For instance, rewrite equations (D.1) as f(x) − 1 = Ψ(x) = 0, multiply componentwise their left- and right-hand sides by x. Evidently, such manipulations give the system of ...