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From the algorithm, we can see that it tries different damping factor until it gets a good one by the error. Is the damping factor related to the eigenvalues of the Hessian matrix?

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The damping factor is expressed in terms of the objective function that one seeks to minimise, as described in A new approach for determining damping factors in Levenberg-Marquardt algorithm for solving an inverse heat conduction problem (2017).

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