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@jemoka / Jemoka Knowledge Base / raw/concept/kbhfixed_point_iteration.md
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--- title: "fixed-point iteration" source: https://www.jemoka.com/posts/kbhfixed_point_iteration/ --- Fixed point iteration is a method for finding a fixed point of a function, which is a value that remains unchanged when the function is applied to it (i.e., f(x) = x). The method works by repeatedly applying the function to an initial guess: Start with an initial approximation x₀ Compute successive iterations: xₙ₊₁ = f(xₙ) Continue until convergence (|xₙ₊₁ - xₙ| < ε) or maximum iterations The method converges if the function is a contraction mapping in the neighborhood of the fixed point (|f’(x)| < 1).