Degree of $L_p$ Approximation by Monotone Splines

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1980 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 11, pages 436-447 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Chui, C. K.; Smith, P. W.; Ward, J. D.;

doi: 10.1137/0511041

Degree of $L_p$ Approximation by Monotone Splines

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Abstract

Using elementary techniques, we obtain Jackson type estimates for the approximation of monotone nondecreasing functions by monotone nondecreasing splines with equally spaced knots in $L_p [0,1],\, 1 \leqq p \leqq \infty $. Our method, which works for all p, is different from that of De Vore.

Keywords

monotone nondecreasing splines, Spline approximation, Jackson type estimates, Rate of convergence, degree of approximation

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