The Lipschitz condition is a mathematical requirement for a function, indicating that there exists a constant $K$ such that for all pairs of points $x_1$ and $x_2$, the absolute difference between the function values is bounded by $K$ times the distance between the points, expressed as $|f(x_1) - f(x_2)| \leq K |x_1 - x_2|$. This concept is crucial in understanding the stability and convergence of numerical methods since it helps ensure that small changes in input lead to controlled changes in output.
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