How is f(x) evaluated for each iteration using fsolve?
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Martijn on 15 Jan 2019
The values shown under f(x) in the iteration table are indeed not literally the function values at that given iteration, you are seeing the square of the norm of the function value vector here; as documented, see:
The reason for this is that "fsolve" can actually solve whole systems of equations where f(x) would then be a whole vector of values. Displaying this whole vector in the table is not really feasible, there is not enough space for that. Hence, instead, a measure is shown which basically summarizes the whole f(x) vector in a single measure which also actually is representative for how good the current solution is.
We could look into whether we can perhaps change the header to ||f(x)||^2 in future releases to better illustrate this.