Approximation of Hypersingular Integral Operators With Cauchy Kernel. (1st September 2016)

• Record Type: Journal Article
• Authors: Aliev, Rashid A.; Gadjieva, Chinara A.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 9(2016)
• Page Start: 1055
• Page End: 1065
• Publication Date: 2016-09-01
• Subjects: Best mean-square approximation -- Cauchy kernel -- hypersingular integral equation -- hypersingular integral operator; 41A35 -- 47A58 -- 65R20 -- 45E05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1185615
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In the present article, the hypersingular integral operator with Cauchy kernel H is approximated by a sequence of operators of a special form, and it is proved that the approximating operators H n strongly converge to the operator H and for an algebraic polynomial of degree not higher than n the operators H n and H coincide. Therefore, the estimate established in this article yields more exact results in terms of the convergence rate than traditional methods. At the end we give the approximate solution of the hypersingular integral equation of the first kind.