An improved method for global solution of nonlinear systems (Q1809077)

Let the function \(\psi: D\subset\mathbb{R}^n\to \mathbb{R}^n\) be continuous and let \(X_0\subset D\) be an \(n\)-dimensional interval vector. Some method for determining all zeros of \(\psi\) which lie in \(X_0\) was presented by the author earlier [ibid. 4, No. 2, 125-146 (1998)]. This method was based on the insertion of \(m\) slack variables so that the system \(\psi(x)= 0\) was transformed to a semiseparable system \(f(y)= 0\) of dimension \(m+n\), which could be solved by an appropriate iterative method. The present paper extends these results, i.e., it is shown that the system \(f(y)= 0\) can be reduced to a system of dimension \(n\) again and that elements of the so-called constraint propagation approach can be applied to improve the computational performance.