L2-approximation of real-valued functions with interpolatory constraints

M. A. Bokhari; M. Iqbal

doi:10.1016/0377-0427(95)00210-3

L₂-approximation of real-valued functions with interpolatory constraints

M. A. Bokhari^*
, M. Iqbal

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

4 Scopus citations

Abstract

We construct the polynomial p*_m,n of degree m which interpolates a given real-valued function f ∈ℒ² [a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L₂-sense over all polynomials of degree ≤ m with the same interpolatory character. It is shown that the L₂-error ∥p*_m,n - f ∥ → 0 as m → ∞ if f ∈ C[a, b].

Original language	English
Pages (from-to)	201-205
Number of pages	5
Journal	Journal of Computational and Applied Mathematics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1016/0377-0427(95)00210-3
State	Published - 28 Jun 1996

Keywords

Interpolation
Least squares approximation
Orthonormal basis
Uniformly dense

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/0377-0427(95)00210-3

Cite this

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title = "L2-approximation of real-valued functions with interpolatory constraints",

abstract = "We construct the polynomial p*m,n of degree m which interpolates a given real-valued function f ∈ℒ2 [a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L2-sense over all polynomials of degree ≤ m with the same interpolatory character. It is shown that the L2-error ∥p*m,n - f ∥ → 0 as m → ∞ if f ∈ C[a, b].",

keywords = "Interpolation, Least squares approximation, Orthonormal basis, Uniformly dense",

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T1 - L2-approximation of real-valued functions with interpolatory constraints

AU - Bokhari, M. A.

AU - Iqbal, M.

PY - 1996/6/28

Y1 - 1996/6/28

N2 - We construct the polynomial p*m,n of degree m which interpolates a given real-valued function f ∈ℒ2 [a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L2-sense over all polynomials of degree ≤ m with the same interpolatory character. It is shown that the L2-error ∥p*m,n - f ∥ → 0 as m → ∞ if f ∈ C[a, b].

AB - We construct the polynomial p*m,n of degree m which interpolates a given real-valued function f ∈ℒ2 [a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L2-sense over all polynomials of degree ≤ m with the same interpolatory character. It is shown that the L2-error ∥p*m,n - f ∥ → 0 as m → ∞ if f ∈ C[a, b].

KW - Interpolation

KW - Least squares approximation

KW - Orthonormal basis

KW - Uniformly dense

UR - https://www.scopus.com/pages/publications/0030172608

U2 - 10.1016/0377-0427(95)00210-3

DO - 10.1016/0377-0427(95)00210-3

M3 - Article

AN - SCOPUS:0030172608

SN - 0377-0427

VL - 70

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EP - 205

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -