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Superlinear convergence theorems for Newton-type methods for nonlinear systems of equations

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In this paper, someQ-order convergence theorems are given for the problem of solving nonlinear systems of equations when using very general finitely terminating methods for the solution of the associated linear systems. The theorems differ from those of Dembo, Eisenstat, and Steihaug in the different stopping condition and in their applicability to the nonlinear ABS algorithm.

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Communicated by L. C. W. Dixon

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Abaffy, J. Superlinear convergence theorems for Newton-type methods for nonlinear systems of equations. J Optim Theory Appl 73, 269–277 (1992). https://doi.org/10.1007/BF00940181

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Key Words

  • Nonlinear systems of equations
  • Newton-type methods
  • truncated-Newton algorithms
  • ABS methods