ON THE USE OF PRODUCT STRUCTURE IN SECANT METHODS FOR NONLINEAR LEAST-SQUARES PROBLEMS

The problem of adjusting the second-order term in secant methods for nonlinear least squares problems with zero-residual is addressed. The author uses the framework of structured secant methods to derive and investigate a new way to resize the approximation of the second-order term using some exact information. The resulting method is a self-adjusting structured secant method for nonlinear least squares problems, yielding a q-quadratic convergence rate for zero residual and a q-superlinear convergence rate for nonzero residual problems.