A derivative-free arc continuation method and a bifurcation technique
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 wordsarc continuation quasi-Newton methods least change secant updates Brouwer degree numerical computation nonlinear algebraic systems Powell's method
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