Solving underdetermined systems with interval methods (Q1300083)

The well-known Krawczyk-operator \(K(X)= x-Yf(x)+ (I- YF'(X))(X- x)\) is frequently used in iterative methods for solving equations \(f(x)= 0\) with \(f:\mathbb{R}^n\to \mathbb{R}^n\), \(x\in X\), where \(Y\) is a nonsingular parameter matrix and \(F'\) is an isotone interval extension of \(f'\). In order to be able to solve equations with \(f: \mathbb{R}^n\to\mathbb{R}^n\), the matrix \(Y\) has to be of type \(n\times m\) and the identity matrix \(I\) is replaced by a product \(YA\) where \(A\) is a matrix of type \(m\times n\) which satisfies \(YAY= Y\).