Ravi Varadhan wrote: > That is not a good approach, i.e. finding the zero, x*, of F(x), such that > F(x*) = 0, as a minimum of ||F(x)|| is NOT a good approach. Any root of > F(x) is indeed a global minimum of ||F(x)||, or for that matter, the global > minimum of any f(F(x)), where f(.) is a mapping from R^p to R, such that it > has a uniques global minimizer x=0. However, the converse does not > generally hold, i.e. a (local) minimizer of f(F(x)) is not necessarily a > root of F(x). See Ortega and Rheinboldt (p. 97, 1970) for theorem on this. > > There are better approaches that directly solve the non-linear system (e.g. > Newton's method and spectral appproaches). There are 2 packages in R that > are quite useful for finding roots of nonlinear systems of equations: "BB" > and "nleqslv". For more information, You can try, for example: > > library(BB) > ?dfsane > > Hope this helps, > Ravi.
Thanks for the correction! I should also clarify that I misremembered
what Numerical Recipes said -- it explains (as you did) why collapsing
does _not_ work well.
cheers
Ben
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