Back to Search
Start Over
On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces
- Source :
- Fract. Calc. Appl. Anal. Vol. 22, No 3 (2019), pp. 699-721
- Publication Year :
- 2018
-
Abstract
- In this paper, we study a fractional-order variant of the asymptotical regularization method, called {\it 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 that under certain smoothness assumptions, FAR with fractional order in the range $(1,2)$ yields an acceleration with respect to comparable order optimal regularization methods. Based on the one-step Adams-Moulton method, a novel iterative regularization scheme is developed for the numerical realization of FAR. Two numerical examples are given to show the accuracy and the acceleration effect of FAR.
- Subjects :
- Mathematics - Numerical Analysis
Subjects
Details
- Database :
- arXiv
- Journal :
- Fract. Calc. Appl. Anal. Vol. 22, No 3 (2019), pp. 699-721
- Publication Type :
- Report
- Accession number :
- edsarx.1812.09734
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1515/fca-2019-0039