Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Nonlinear algebraic equations and numerical solution of the transcendental equation

On the Complexity of the Modified Levenberg-Marquardt Algorithm for Nonlinear Equations

Author XiGuoTai
Tutor FanJinYan
School Shanghai Jiaotong University
Course Computational Mathematics
Keywords Levenberg-Marquardt method singular nonlinearequations complexity bound
CLC O241.7
Type Master's thesis
Year 2012
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We propose a new modified Levenberg-Marquardt algorithm for the system ofnonlinear equationsF(x) = 0.The Levenberg-Marquardt parameter is chosen as ||Fk||δwhereδis a positive constant. The new algorithm is globally convergent under somesuitable conditions.Under the local error bound condition which is weaker than thenonsingularity,we show that the new algorithm converges superlinearly to the solutionforδ∈(0, 1),while quadratically for anyδ∈[1, 2].We also prove that the globalcomplexity bound of the new algorithm is O(-2).Numerical results show that thenew algorithm performs well for some singular problems.

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