Numerical conditioning for nonlinear least square.
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Author:  solarbike [ Fri Aug 19, 2011 2:30 pm ]
Post subject:  Numerical conditioning for nonlinear least square.

The Levenberg-Marquardt method requires inverting the approximate Hessian J^T*J (J = jacobian). In most cases where J has full column rank, the Hessian has full rank and the inverse exist. However, what if the approximated Hessian has poor condition number (i.e. the ratio between the largest and smallest singular value is greater, say, 1e6?) The solution of the decent direction is highly sensitive to data if the condition number if big. Doe the Levenberg-Marquardt method in ALGLIB has some kind of conditioning mechanism to ease this problem?

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