if the chord method
x_{n+1}=x_n – (J_o)^{-1} f(x_n)
converges, can we then be sure that the Broyden update method
x_{n+1}=x_n – (J_n)^{-1} f(x_n)
starting from the same initial Jacobian converges ?
Thx
H.E. Lehtihet
I don't think we can be sure of that. It seems to me that it all depends not only on the landscape but also on the starting point. It should not be too difficult to find a simple 2D counterexample for which the chord method will easily converge whereas the Broyden update method will not (and v.v).
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Rob Haelterman
Thanks for your answer. And yes, indeed, you are absolutely right. Having worked on the matter some more after my question, we've been able to find examples of both. It's not the answer I had hoped for, but it's an answer. Kind regards, Rob
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