On Fractional Asymptotical Regularization of Linear Ill-Posed Problems in Hilbert Spaces

• Published in: Fractional calculus & applied analysis Vol. 22; no. 3; pp. 699 - 721
• Main Authors: Zhang, Ye, Hofmann, Bernd
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 26.06.2019; De Gruyter; Walter de Gruyter GmbH
• Subjects: 65F22; 65J20; 65R30; Abstract Harmonic Analysis; Acceleration; Analysis; Asymptotic properties; asymptotical regularization; convergence rates; fractional derivatives; Functional Analysis; Hilbert space; Ill posed problems; Integral Transforms; Iterative methods; linear ill-posed operator equation; Mathematics; Operational Calculus; Primary 47A52; Secondary 26A33; Regularization; Regularization methods; Research Paper; Smoothness; source conditions; stopping rules; 65R30; linear ill-posed operator equation; fractional derivatives; Primary 47A52; 65F22; Secondary 26A33; stopping rules; source conditions; 65J20; asymptotical regularization; convergence rates, acceleration

In this paper, we study a fractional-order variant of the asymptotical regularization method, called Fractional Asymptotical Regularization (FAR) , for solving linear ill-posed operator equations in a Hilbert space setting. We assign the method to the general linear regularization schema and prove t...