There is not only one-way to do fixed point iteration. The problem description needs improvement by perhaps adding that x_n = g(x_n-1).
Find the two most distant points
Given area find sides
Back to basics - mean of corner elements of a matrix
False position (linear interpolation) method of finding a root.
Free Fall analytical solution (Chapra 2012 textbook Example 1.1)
Fletcher-Reeves Conjugate Gradient Method
Steepest Descent Method
Rosenbrock's Banana Function and its derivatives
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