Levenberg--Marquardt algorithm: implementation and theory
Levenberg--Marquardt algorithm: implementation and theory The nonlinear least-squares minimization problem is considered. Algorithms for the numerical solution of this problem have been proposed in the past, notably by Levenberg (Quart. Appl. Math., 2, 164-168 (1944)) and Marquardt (SIAM J. Appl. Math., 11, 431-441 (1963)). The present work discusses a robust and efficient implementation of a version of the Levenberg--Marquardt algorithm and shows that it has strong convergence properties. In addition to robustness, the main features of this implementation are the proper use of implicitly scaled variables and the choice of the Levenberg--Marquardt parameter by means of a scheme due to Hebden (AERE Report TP515). Numerical results illustrating the behavior of this implementation are included. 1 table. (RWR)
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