The L2 norm of the approximation error for Bernstein polynomials

Douglas H. Jones

doi:10.1016/0021-9045(76)90001-0

The L₂ norm of the approximation error for Bernstein polynomials

Douglas H. Jones

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

1 Scopus citations

Abstract

Wassily Hoeffding (J. Approximation Theory 4 (1971), 347-356) obtained a convergence rate for the L₁ norm of the approximation error, using Bernstein polynomials for a wide class of functions. Here, by a different method of proof, a similar result is obtained for the L₂ norm.

Original language	English (US)
Pages (from-to)	307-315
Number of pages	9
Journal	Journal of Approximation Theory
Volume	18
Issue number	4
DOIs	https://doi.org/10.1016/0021-9045(76)90001-0
State	Published - Dec 1976
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1016/0021-9045(76)90001-0

Cite this

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title = "The L2 norm of the approximation error for Bernstein polynomials",

abstract = "Wassily Hoeffding (J. Approximation Theory 4 (1971), 347-356) obtained a convergence rate for the L1 norm of the approximation error, using Bernstein polynomials for a wide class of functions. Here, by a different method of proof, a similar result is obtained for the L2 norm.",

author = "Jones, {Douglas H.}",

note = "Funding Information: * Research supported by a Summer Fellowship from the Research Council, Rutgers University.",

year = "1976",

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PY - 1976/12

Y1 - 1976/12

N2 - Wassily Hoeffding (J. Approximation Theory 4 (1971), 347-356) obtained a convergence rate for the L1 norm of the approximation error, using Bernstein polynomials for a wide class of functions. Here, by a different method of proof, a similar result is obtained for the L2 norm.

AB - Wassily Hoeffding (J. Approximation Theory 4 (1971), 347-356) obtained a convergence rate for the L1 norm of the approximation error, using Bernstein polynomials for a wide class of functions. Here, by a different method of proof, a similar result is obtained for the L2 norm.

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JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

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ER -

The L₂ norm of the approximation error for Bernstein polynomials

Abstract

All Science Journal Classification (ASJC) codes

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