Solution of nonlinear least squares problems by approximate Gauss-Newton methods

For minimizing a functional phi(x) = 1/2 \\F(x)\\(2), where F is Frechet-differentiable operator from a Hilbert space H-1 into another H-2. approximate Gauss-Newton type methods based on the use of IU-weighted or WI-weighted pseudoinverse are developed. The approach adopted by this report is the use of approximations for inverses or approximate solutions for the corresponding linear equations at inner iterations with the Gauss-Newton method as outer iteration. Their convergence properties and computational aspects are described as well as questions of preconditioning are discussed.