Node:Overview of Nonlinear Least-Squares Fitting, Next:Initializing the Nonlinear Least-Squares Solver, Up:Nonlinear Least-Squares Fitting

The problem of multidimensional nonlinear least-squares fitting requires the minimization of the squared residuals of n functions, f_i, in p parameters, x_i,

All algorithms proceed from an initial guess using the linearization,

where x is the initial point, p is the proposed step and J is the Jacobian matrix J_{ij} = d f_i / d x_j. Additional strategies are used to enlarge the region of convergence. These include requiring a decrease in the norm ||F|| on each step or using a trust region to avoid steps which fall outside the linear regime.