Shape-preserving smoothing of 3-convex splines of degree 4

被引：0

作者：

Prymak A.V. ^{[1
]}

机构：

[1] Shevchenko Kyiv National University, Kyiv

来源：

Ukrainian Mathematical Journal | 2005年 / 57卷 / 2期

关键词：

Absolute Constant;

D O I：

10.1007/s11253-005-0193-8

中图分类号：

学科分类号：

摘要：

For every 3-convex piecewise-polynomial function s of degree ≤4 with n equidistant knots on [0, 1] we construct a 3-convex spline s 1 (s 1 C (3)) of degree ≤4 with the same knots that satisfies the inequality ||S - S 1 || C0,1] ≤ ω 5 (s;1/n), where c is an absolute constant and ω 5 is the modulus of smoothness of the fifth order. © 2005 Springer Science+Business Media, Inc.

引用

页码：331 / 339

页数：8

共 12 条

[1]

Roberts A.W., Varbeg D.E., Convex Functions, (1973)

[2]

DeVore R.A., Monotone approximation by splines, SIAM J. Math. Anal., 8, 5, pp. 891-905, (1977)

[3]

Beatson R.K., Convex approximation by splines, SIAM J. Math. Anal., 12, pp. 549-559, (1981)

[4]

Hu Y.K., Convex approximation by quadratic splines, J. Approxim. Theor., 74, pp. 69-82, (1993)

[5]

Kopotun K.A., Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials, Contstr. Approxim., 10, pp. 153-178, (1994)

[6]

Shevchuk I.A., One construction of cubic convex spline, Proc. ICAOR, 1, pp. 357-368, (1997)

[7]

Konovalov V.N., Leviatan D., Shape-preserving widths of Sobolev-type classes of s-monotone functions on a finite interval, Isr. J. Math., 133, pp. 239-268, (2003)

[8]

Konovalov V.N., Leviatan D., Estimates on the approximation of 3-monotone function by 3-monotone quadratic splines, East J. Approxim., 7, pp. 333-349, (2001)

[9]

Prymak A.V., Three-convex approximation by quadratic splines with arbitrary fixed knots, East J. Approxim., 8, 2, pp. 185-196, (2002)

[10]

Leviatan D., Prymak A.V., On 3-monotone approximation by piecewise polynomials, J. Approxim. Theor., 133, pp. 97-121, (2005)

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