Mathematical Programming

, Volume 35, Issue 1, pp 71–82

Broyden's method in Hilbert space

  • Ekkehard W. Sachs

DOI: 10.1007/BF01589442

Cite this article as:
Sachs, E.W. Mathematical Programming (1986) 35: 71. doi:10.1007/BF01589442


Broyden's method is formulated for the solution of nonlinear operator equations in Hilbert spaces. The algorithm is proven to be well defined and a linear rate of convergence is shown. Under an additional assumption on the initial approximation for the derivative we prove the superlinear rate of convergence.

Key words

Broyden's methodquasi-Newton methodssuperlinear convergence rate

Copyright information

© The Mathematical Programming Society, Inc. 1986

Authors and Affiliations

  • Ekkehard W. Sachs
    • 1
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA