The worst case complexity of the fredholm equation of the second kind with non-periodic free term and noise information

• Published in: Numerical functional analysis and optimization Vol. 19; no. 3-4; pp. 329 - 343
• Main Author: Jiang, Tianzi
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Marcel Dekker, Inc 01.01.1998; Taylor & Francis
• Subjects: AMS subject classification: 45B05; AMS subject classification: 65R20; Complexity; Exact sciences and technology; Finite element information; Finite element method; Fredholm equation of the second kind; Integral equations; Integral equations, integral transforms; Mathematical analysis; Mathematics; Noise information; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Finite element method; Finite element information; Worst case; Noise; Integral equation; Noise information; Equation of second kind; Complexity; Fredholm equation
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630569808816831

This paper deals with the complexity of the Fredholm equation of the second kind with . The problem elements are free term f and belong to the unit ball of [math03]. Available information about the problem consists of evaluations of f and is assumed to be corrupted by uniformly bounded noise. The absolute error in each noisy evaluation is at most δ. First, we give estimation of the n-th optimal radius in the worst case setting. Then, we show that a noisy finite element method with quadrature (FEMQ) has minimal error. Finally, we give the estimate of €complexity of Fredholm problem of the second kind in the worst case setting. To the best of our knowledge, this is the first work on complexity of integral equation with noisy information