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Global analysis of continuous analogues of the Levenberg-Marquardt and Newton-Raphson methods for solving nonlinear equations

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Global analyses are given to continuous analogues of the Levenberg-Marquardt methoddx/dt=−(J t(x)J(x)+δI)−1Jt(x)g(x), and the Newton-Raphson-Ben-Israel methoddx/dt=−J +(x)g(x), for solving an over- and under-determined systemg(x)=0 of nonlinear equations. The characteristics of both methods are compared. Erros in some literature which dealt with related continous analogue methods are pointed out.

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Authors
  1. Kunio Tanabe
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Tanabe, K. Global analysis of continuous analogues of the Levenberg-Marquardt and Newton-Raphson methods for solving nonlinear equations. Ann Inst Stat Math 37, 189–203 (1985). https://doi.org/10.1007/BF02481091

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  • DOI: https://doi.org/10.1007/BF02481091

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