GNU Scientific Library – Reference Manual: Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient

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#### 39.2.6 Steihaug-Toint Conjugate Gradient

One difficulty of the dogleg methods is calculating the Gauss-Newton step when the Jacobian matrix is singular. The Steihaug-Toint method also computes a generalized dogleg step, but avoids solving for the Gauss-Newton step directly, instead using an iterative conjugate gradient algorithm. This method performs well at points where the Jacobian is singular, and is also suitable for large-scale problems where factoring the Jacobian matrix could be prohibitively expensive.