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).
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Sum the Digits of a Number
04 - Scalar Equations 1
Forward Elimination for Gauss Elimination
Bisection method of finding a root.
Steepest Descent Method
Sequential Unconstrained Minimization (SUMT) using Exterior Penalty
False position (linear interpolation) method of finding a root.
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