On the order of convergence of Broyden-Gay-Schnabel's method

J. M. Martínez

Commentationes Mathematicae Universitatis Carolinae (1978)

  • Volume: 019, Issue: 1, page 107-118
  • ISSN: 0010-2628

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Martínez, J. M.. "On the order of convergence of Broyden-Gay-Schnabel's method." Commentationes Mathematicae Universitatis Carolinae 019.1 (1978): 107-118. <http://eudml.org/doc/16886>.

@article{Martínez1978,
author = {Martínez, J. M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
language = {eng},
number = {1},
pages = {107-118},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the order of convergence of Broyden-Gay-Schnabel's method},
url = {http://eudml.org/doc/16886},
volume = {019},
year = {1978},
}

TY - JOUR
AU - Martínez, J. M.
TI - On the order of convergence of Broyden-Gay-Schnabel's method
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1978
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 019
IS - 1
SP - 107
EP - 118
LA - eng
UR - http://eudml.org/doc/16886
ER -

References

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  1. J. G. P. BARNES, An algorithm for solving nonlinear equations based on the secant method, Computer Journal, 8, 1965, 66-72. (1965) MR0181101
  2. C. G. BROYDEN, A class of methods for solving nonlinear simultaneous equations, Mathematics of Computation, 19, 1965, 577-593. (1965) Zbl0131.13905MR0198670
  3. J. E. DENNIS J. J. MORE, A characterization of superlinear convergence and its application to quasi-Newton methods, Mathematics of Computation, 28, 1974, 549-560. (1974) MR0343581
  4. D. M. GAY, Some convergence properties of Broyden's method, Working Paper No 175, National Bureau of Economic Research, USA, 1977. (1977) 
  5. D. M. GAY R. B. SCHNABEL, Solving systems of non-linear equations by Broyden's method with projected updates, Working Paper No 169, National Bureau of Economic Research, USA, 1977. (1977) 
  6. W. B. GRAGG G. W. STEWART, A stable variant of the secant method for solving nonlinear equations, SIAM J. of Numerical Analysis, 13, 1976, 127-140. (1976) MR0433856
  7. J. J. MORE J. TRAGENSTEIN, On the global convergence of Broyden's method, Mathematics of Computation, 30, 1976, 523-540. (1976) MR0418451
  8. J. M. ORTEGA W. C. RHEINBOLDT, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. (1970) MR0273810
  9. M. J. D. POWELL, A hybrid method for nonlinear equations, en Rabinovitz P. (editor), Numerical methods for nonlinear algebraic equations, Gordon and Breach, London, 1970. (1970) Zbl0277.65028MR0343589
  10. P. WOLFE, The secant method for solving nonlinear equations, Communications ACM, 12, 1959, 12-13. (1959) 

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