caa a22 4500 606167382 CHVBK 20210128100702.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10665-013-9671-4 doi (NATIONALLICENCE)springer-10.1007/s10665-013-9671-4 Fractional regularization matrices for linear discrete ill-posed problems [Elektronische Daten] [Michiel Hochstenbach, Silvia Noschese, Lothar Reichel] The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices $$A^\mathrm{T}\!A$$ A T A (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small- and large-scale problems are considered. Springer Science+Business Media Dordrecht, 2013 Fractional Lavrentiev regularization nationallicence Fractional power regularization matrix nationallicence Fractional Tikhonov regularization nationallicence Ill-posed problem nationallicence Hochstenbach Michiel Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600MB, Eindhoven, The Netherlands aut Noschese Silvia Dipartimento di Matematica "Guido Castelnuovo”, SAPIENZA Università di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy aut Reichel Lothar Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 113-129 0022-0833 93:1<113 2015 93 10665 https://doi.org/10.1007/s10665-013-9671-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-013-9671-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hochstenbach Michiel Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600MB, Eindhoven, The Netherlands aut NATIONALLICENCE 700 1- Noschese Silvia Dipartimento di Matematica "Guido Castelnuovo”, SAPIENZA Università di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy aut NATIONALLICENCE 700 1- Reichel Lothar Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 113-129 0022-0833 93:1<113 2015 93 10665