A modified Levenberg-Marquardt method with line search for nonlinear equations
To save more Jacobian calculations and achieve a faster convergence rate a new modified Levenberg-Marquardt (LM) method for nonlinear equations is presented. At every iteration, not only the accelerating trial step but also an additional LM step which uses the previous available Jacobian instead of the new Jacobian, is computed in this new method. Under the local error bound condition which is weaker than nonsingularity, the new method has fourth convergence rate. Results of numerical tests are given.
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