Optimal Approximation of Functions: Chebyshev-type ApproximationsUniversity of Wisconsin--Madison, 1963 - 172 pages |
Common terms and phrases
a₁ additional approximation is unique approximation to f arbitrary argument assume assumption B₂ Banach space best approximation called chapter Chebyshev system closed compact computational consider constants contains at least continuous contradicts convex Corollary critical point d₁ defined Definition derivatives determined Entl error evident example exists expression Find finite follows function give given Hence holds hypotheses implies inequalities interpolation Lemma Let W(x M[P f methods minimal set minus extremal Moreover neighborhood ordinary Chebyshev approximation polynomial possible prescribed problem Proof proof is complete properties proved respect satisfies Condition sequence signed extremal similar solution space subset Suppose Table Theorem thesis tion true U(xo uniform norm values vector W[xo x₁ zero extremal α α α β αε