ABSTRACT
Nonlinear least squares problems arise in many applications, in particular data fitting and parameter estimation. While the Broyden formula is often thought of as a matrix update, it is really a method for approximating the gradients of the otherwise unrelated component functions of g. According to the proposition tiny perturbations of the approximating Jacobian at a nonstationary fixed point can lead to a small step in the variable vector that results in a significant matrix correction, which in turn effects a sizable change of the variables on the subsequent iteration. Since the iterative solution of the one-dimensional minimization problem could be quite costly, one prefers to accept values for ak that satisfy considerably weaker line-search conditions.
