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).
Project Euler: Problem 3, Largest prime factor
Change the sign of even index entries of the reversed vector
calculate linear convolution two vectors
Free Fall analytical solution (Chapra 2012 textbook Example 1.1)
Augmented Lagrange Multiplier (ALM) Method
Forward Elimination for Gauss Elimination
Steepest Descent Method
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