Quasi-Newton Methods for Nonlinear Least Squares Focusing on Curvatures

A new quasi-Newton method for nonlinear least squares problems is proposed. Two advantages of the method are accomplished by utilizing special geometrical properties in the problem class. First, fast convergence is established for well-conditioned problems by interpolating both the current and the previous step in each iteration. Second, high accuracy is achieved for certain difficult problems, such as ill-conditioned problems and problems with large curvatures in the tangent space. Numerical results for artificial problems and standard test problems are presented and discussed.