Dennis, J.E. Jr.Songbai, ShengVu, Phuong Ahn2018-06-182018-06-181985-02Dennis, J.E. Jr., Songbai, Sheng and Vu, Phuong Ahn. "A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems." (1985) <a href="https://hdl.handle.net/1911/101578">https://hdl.handle.net/1911/101578</a>.https://hdl.handle.net/1911/101578In this paper, we develop, analyze, and test a new algorithm for nonlinear least-squares problems. The algorithm uses a BFGS update of the Gauss-Newton Hessian when some heuristics indicate that the Gauss-Newton method may not make a good step. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method does not build up a Hessian approximation over several steps. The algorithm can be implemented easily as a modification of any Gauss-Newton code, and it seems to be useful for large residual problems27 ppengTechnical reportTR85-01