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A Shamanskii-like Levenberg-Marquardt method for nonlinear equations


  • Jinyan Fan



In this paper, we propose a Shamanskii-like Levenberg-Marquardt method for nonlinear equations. At every iteration, not only a LM step but also m−1 approximate LM steps are computed, where m is a positive integer. Under the local error bound condition which is weaker than nonsingularity, we show the Shamanskii-like LM method converges with Q-order m+1. The trust region technique is also introduced to guarantee the global convergence of the method. Since the Jacobian evaluation and matrix factorization are done after every m computations of the step, the overall cost of the Shamanskii-like LM method is usually much less than that of the general LM method (the m=1 case). Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Jinyan Fan, 2013. "A Shamanskii-like Levenberg-Marquardt method for nonlinear equations," Computational Optimization and Applications, Springer, vol. 56(1), pages 63-80, September.
  • Handle: RePEc:spr:coopap:v:56:y:2013:i:1:p:63-80
    DOI: 10.1007/s10589-013-9549-4

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