 ##  [Fixed-Point Iteration](/fixed-point-iteration) 

  ##  [Fixed-Point Iteration](https://mathlogic.quantumdictionary.io/fixed-point-iteration-0) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

An iterative procedure that seeks a fixed point x = G(x) of a mapping G by repeatedly applying G to an initial guess: x_{k+1} = G(x_k). Convergence depends on contractivity or related properties of G.