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I thought the truncated Chebyshev series of an arbitrary function minimizes the L-inf error among all polynomials of the same degree, because Chebyshev polynomi
by ArbitraryLimits 14y ago
I thought the truncated Chebyshev series of an arbitrary function minimizes the L-inf error among all polynomials of the same degree, because Chebyshev polynomials have minimum L-inf norm among all monic polynomials of the same degree.
Let's try this: Tell me how you would construct a minimax approximation according to your definition?
- stephencanon 14y agoThe truncated Chebyshev series does not generally minimize the L-inf error among all polynomials of the same degree (unless the function being approximated is a polynomial of degree n+1). Constructing a minimax approximation is typically done via the Remez exchange algorithm, which is iterative, fussy, and prone to convergence failures. However, none of those matter when designing an offline approximation as is the case when you're writing math library functions.
- ArbitraryLimits 14y agoThank you, that was enlightening.