A doubly relaxed minimal-norm Gauss–Newton method for underdetermined nonlinear least-squares problems

When a physical system is modeled by nonlinear function, the unknown parameters can be estimated fitting experimental observations least-squares approach. Newton's method and its variants are often used to solve problems of this type. In paper, we concerned with computation minimal-norm solution an underdetermined problem. We present Gauss-Newton type method, which relies on two relaxation ensure convergence, incorporates procedure dynamically estimate parameters, as well rank Jacobian matrix, along iterations. Numerical results presented.