The minimax property refers to a characteristic of certain functions, particularly in approximation theory, where the maximum deviation between the function and its approximating polynomial (or rational function) is minimized. This property is crucial as it ensures that the worst-case error in approximation is as small as possible, leading to a more reliable representation of the target function. The minimax property is especially relevant when discussing Chebyshev polynomials and rational functions, as they are designed to achieve this optimal approximation by minimizing the maximum error across a specific interval.
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