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On the global convergence of Broyden's method

Publication ,  Journal Article
More, JJ; Trangenstein, JA
Published in: Math. Comput. (USA)
1976

Considers Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Q-superlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to R-superlinear convergence provided the search directions form a uniformly linearly independent sequence. The authors then explore this last concept and its connection with Broyden's method. Finally, the authors point out how the above results extend to Powell's symmetric version of Broyden's method

Duke Scholars

Published In

Math. Comput. (USA)

Publication Date

1976

Volume

30

Issue

135

Start / End Page

523 / 540

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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More, J. J., & Trangenstein, J. A. (1976). On the global convergence of Broyden's method. Math. Comput. (USA), 30(135), 523–540.
More, J. J., and J. A. Trangenstein. “On the global convergence of Broyden's method.” Math. Comput. (USA) 30, no. 135 (1976): 523–40.
More JJ, Trangenstein JA. On the global convergence of Broyden's method. Math Comput (USA). 1976;30(135):523–40.
More, J. J., and J. A. Trangenstein. “On the global convergence of Broyden's method.” Math. Comput. (USA), vol. 30, no. 135, 1976, pp. 523–40.
More JJ, Trangenstein JA. On the global convergence of Broyden's method. Math Comput (USA). 1976;30(135):523–540.

Published In

Math. Comput. (USA)

Publication Date

1976

Volume

30

Issue

135

Start / End Page

523 / 540

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics