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

All algorithms proceed from an initial guess using the linearization,

where @math{x} is the initial point, @math{p} is the proposed step and @math{J} is the Jacobian matrix @c{$J_{ij} = \partial f_i / \partial x_j$} @math{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 @math{||F||} on each step or using a trust region to avoid steps which fall outside the linear regime.

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