A Derivative-Free Nonlinear Least Squares Solver.

An improved version of derivative-free nonlinear least squares iterative solver developed earlier by the author is described. First, we apply a regularization technique to stabilize the evaluation of search directions similar to the one used in the Levenberg-Marquardt methods. Second, we propose several modified designs for the rectangular preconditioning matrix, in particular a sparse adaptive techniques avoiding the use of pseudorandom sequences. The resulting algorithm is based on easily parallelizable computational kernels such as dense matrix factorizations and elementary vector operations thus having a potential for an efficient implementation on modern high-performance computers. Numerical results are presented for several standard test problems as well as for some special complex-valued cases to demonstrate the effectiveness of the proposed improvements to method.