Best L2 Local Approximation on Two Small Intervals. (1st February 2016)

• Record Type: Journal Article
• Authors: Cuenya, H. H.; Ferreyra, D. E.; Ridolfi, C. V.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 2(2016)
• Page Start: 145
• Page End: 158
• Publication Date: 2016-02-01
• Subjects: Algebraic polynomials -- best local approximation -- L2 differentiability; 41A50 -- 41A10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1091777
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we introduce the τ condition, which is weaker than the L 2 differentiability. If a function satisfies the τ condition on two points of ℝ, we prove the existence and characterization of the best local polynomial approximation on these points.