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A derivative-free arc continuation method and a bifurcation technique

  • R. B. Kearfott
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 878)

Abstract

Algorithms and comparison results for a derivative-free predictor-corrector method for following arcs of H(x,t) = ϑ, where H : Rn × [0, 1] → Rn is smooth, are given. The method uses a least-change secant update for H', adaptive controlled predictor stepsize, and Powell's indexing procedure to preserve linear independence in the updates. Considerable savings in numbers of theoretical function calls are observed over high order methods requiring explicit H'. The framework of a promising technique for handling general bifurcation problems is presented.

key words

arc continuation quasi-Newton methods least change secant updates Brouwer degree numerical computation nonlinear algebraic systems Powell's method 

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • R. B. Kearfott
    • 1
  1. 1.Department of MathematicsUniversity of Southwestern LouisianaLafayetteUSA

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