Contraction map

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Also called a contractor. A function that brings points closer together, forming the foundation for convergence by successive approximation. Mathematically, we have LaTeX: f: X \rightarrow X, where LaTeX: X is in a normed space, with norm of LaTeX: x denoted by LaTeX: \|x\|. LaTeX: f is a contractor if there exists a constant LaTeX: K in LaTeX: [0,1) such that LaTeX: \|f(x)-f(y)\| \le K \|x-y\| for all LaTeX: x and LaTeX: y in LaTeX: X. See the supplement on fixed points.


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