On the Jacobian of a Function at a Zero Computed by a Fixed Point Algorithm

Eaves and Scarf, and independently Todd, proved that the determinant of the Jacobian of a function at a zero computed by a fixed-point algorithm was zero or had the same sign as that of the artificial function used to start the algorithm. Here we show that any matrix satisfying this sign property can be realized as the Jacobian of a function at such a computed zero.