Levenberg–Marquardt algorithm: Difference between revisions

Content deleted Content added
m under Gauss-Newton method → under the Gauss-Newton method; a set <math>n</math> linear equations → a set of <math>n</math> linear equations
m Geodesic acceleration: it does not require to compute → it does not require computing {impersonal use of "require" + gerund}
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Since this geodesic acceleration term depends only on the [[directional derivative]] <math>f_{vv} = \sum_{\mu\nu} v_{\mu} v_{\nu} \partial_{\mu} \partial_{\nu} f (\boldsymbol{x})</math> along the direction of the velocity <math>\boldsymbol{v}</math>, it does not require to computecomputing the full second order derivative matrix, requiring only a small overhead in terms of computing cost.<ref>{{cite web|url=https://www.gnu.org/software/gsl/doc/html/nls.html|title=Nonlinear Least-Squares Fitting|publisher=GNU Scientific Library|archive-url=https://web.archive.org/web/20200414204913/https://www.gnu.org/software/gsl/doc/html/nls.html|archive-date=2020-04-14}}</ref> Since the second order derivative can be a fairly complex expression, it can be convenient to replace it with a [[finite difference]] approximation
 
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