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- W2049020275 abstract "Let Snk,r denote the collection of polynomial splines of order k with at most (n − 1) free knots, each of multiplicity r. This paper explicitly finds the constants Ck,r,p so that limn→∞nkdistLp[0, 1]{ƒ, Snk,r} = Ck,r,p ∥ƒ(k)∥Lσ[0,1], where σ = p(kp + 1)and ƒ is sufficiently smooth. This completely fills the gap between previously known results for simple knots (r = 1) and for piecewise polynomials (r = k). We also consider similar asymptotic properties pertaining to approximation of vector functions by vector splines. We define the latter to be families of vector functions whose components are splines of order k with common knots." @default.
- W2049020275 created "2016-06-24" @default.
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- W2049020275 date "1987-01-01" @default.
- W2049020275 modified "2023-09-27" @default.
- W2049020275 title "Further asymptotic properties of best approximation by splines" @default.
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- W2049020275 doi "https://doi.org/10.1016/0021-9045(87)90109-2" @default.
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