Positive and copositive spline approximation in Lp[0, 1]

Y. K. Hu

doi:10.1016/0898-1221(95)00091-7

Positive and copositive spline approximation in L_p[0, 1]

Y. K. Hu

Emeriti, Retired, & In Memoriam (COSM)

Georgia Southern University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The order of positive and copositive spline approximation in the L_p-norm, 1 ≤ p < ∞, is studied; the main results are 1. (1) the error of positive approximation by splines is bounded by Cω₂(f, 1 n)_p if f has a nonnegative extension; 2. (2) the order deteriorates to ω₁ if f does not have such an extension; 3. (3) the error of copositive spline approximation is bounded by Cω(f, 1 n)_p; 4. (4) if f is also continuous, the error in (3) can be estimated in terms of the third τ-modulus τ₃(f, 1 n)_p. All constants in the error bounds are absolute.

Original language	English
Pages (from-to)	137-146
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	30
Issue number	3-6
DOIs	https://doi.org/10.1016/0898-1221(95)00091-7
State	Published - Sep 1995

Keywords

Constrained approximation in L space
Degree of copositive approximation
Polynomial approximation
Spline approximation

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10.1016/0898-1221(95)00091-7

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title = "Positive and copositive spline approximation in Lp[0, 1]",

abstract = "The order of positive and copositive spline approximation in the Lp-norm, 1 ≤ p < ∞, is studied; the main results are 1. (1) the error of positive approximation by splines is bounded by Cω2(f, 1 n)p if f has a nonnegative extension; 2. (2) the order deteriorates to ω1 if f does not have such an extension; 3. (3) the error of copositive spline approximation is bounded by Cω(f, 1 n)p; 4. (4) if f is also continuous, the error in (3) can be estimated in terms of the third τ-modulus τ3(f, 1 n)p. All constants in the error bounds are absolute.",

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T1 - Positive and copositive spline approximation in Lp[0, 1]

AU - Hu, Y. K.

PY - 1995/9

Y1 - 1995/9

N2 - The order of positive and copositive spline approximation in the Lp-norm, 1 ≤ p < ∞, is studied; the main results are 1. (1) the error of positive approximation by splines is bounded by Cω2(f, 1 n)p if f has a nonnegative extension; 2. (2) the order deteriorates to ω1 if f does not have such an extension; 3. (3) the error of copositive spline approximation is bounded by Cω(f, 1 n)p; 4. (4) if f is also continuous, the error in (3) can be estimated in terms of the third τ-modulus τ3(f, 1 n)p. All constants in the error bounds are absolute.

AB - The order of positive and copositive spline approximation in the Lp-norm, 1 ≤ p < ∞, is studied; the main results are 1. (1) the error of positive approximation by splines is bounded by Cω2(f, 1 n)p if f has a nonnegative extension; 2. (2) the order deteriorates to ω1 if f does not have such an extension; 3. (3) the error of copositive spline approximation is bounded by Cω(f, 1 n)p; 4. (4) if f is also continuous, the error in (3) can be estimated in terms of the third τ-modulus τ3(f, 1 n)p. All constants in the error bounds are absolute.

KW - Constrained approximation in L space

KW - Degree of copositive approximation

KW - Polynomial approximation

KW - Spline approximation

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U2 - 10.1016/0898-1221(95)00091-7

DO - 10.1016/0898-1221(95)00091-7

M3 - Article

AN - SCOPUS:0011630287

SN - 0898-1221

VL - 30

SP - 137

EP - 146

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 3-6

ER -

Positive and copositive spline approximation in L_p[0, 1]

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Keywords

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