GNU Scientific Library – Reference Manual: Nonlinear Least-Squares TRS 2D Subspace

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#### 39.2.5 Two Dimensional Subspace

The dogleg methods restrict the search for the TRS solution to a 1D curve defined by the Cauchy and Gauss-Newton points. An improvement to this is to search for a solution using the full two dimensional subspace spanned by the Cauchy and Gauss-Newton directions. The dogleg path is of course inside this subspace, and so this method solves the TRS at least as accurately as the dogleg methods. Since this method searches a larger subspace for a solution, it can converge more quickly than dogleg on some problems. Because the subspace is only two dimensional, this method is very efficient and the main computation per iteration is to determine the Gauss-Newton point.