minimax polynomial approximations
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§3.11(i) Minimax Polynomial Approximations… ►If we have a sufficiently close approximation … ►For examples of minimax polynomial approximations to elementary and special functions see Hart et al. (1968). … ►Since , is a monotonically increasing function of , and (for example) , this means that in practice the gain in replacing a truncated Chebyshev-series expansion by the corresponding minimax polynomial approximation is hardly worthwhile. … ►The theory of polynomial minimax approximation given in §3.11(i) can be extended to the case when is replaced by a rational function . …
Hastings (1955) gives several minimax polynomial and rational approximations for , and the auxiliary functions and .
§18.38(i) Classical OP’s: Numerical Analysis►
Approximation Theory►The scaled Chebyshev polynomial , , enjoys the “minimax” property on the interval , that is, has the least maximum value among all monic polynomials of degree . … ►
Integrable Systems… ►Ultraspherical polynomials are zonal spherical harmonics. …
Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
Piessens and Branders (1972) gives the coefficients of the Chebyshev-series expansions of and , , for (23D).