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From: Gunter Winkler (guwi17_at_[hidden])
Date: 2006-10-24 14:16:07

Hi Fred and Karl,

Karl Meerbergen schrieb:
> I vaguely recall that conjugate gradients is an optimization method. But I do
> not recall the details for nonlinear problems. Convergence is only guaranteed
> for specific math properties, as this is also the case for linear systems.

Yes. Linear CG is a method to find (the unique) vector x that minimizes
a (scalar) quadratic function

f(x) := 1/2 <x, Ax> - <b, x> -> min

( <a,b> is any inner product, such that <x, Ax> > 0 for all x<>0 )

Although I must admit that I never heard of "the nonlinear CG". There
are lots of gradient based methods for nonlinear minimization.

Fred, can you explain your method?