caa a22 4500 445862041 CHVBK 20180317145446.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10092-010-0030-9 doi (NATIONALLICENCE)springer-10.1007/s10092-010-0030-9 A hybrid multilevel-active set method for large box-constrained linear discrete ill-posed problems [Elektronische Daten] [S. Morigi, R. Plemmons, L. Reichel, F. Sgallari] Many questions in science and engineering give rise to linear ill-posed problems, whose solution is known to satisfy box constraints, such as nonnegativity. The solution of discretized versions of these problems is highly sensitive to perturbations in the data, discretization errors, and round-off errors introduced during the computations. It is therefore often beneficial to impose known constraints during the solution process. This paper describes a two-phase algorithm for the solution of large-scale box-constrained linear discrete ill-posed problems. The first phase applies a cascadic multilevel method and imposes the constraints on each level by orthogonal projection. The second phase improves the computed approximate solution on the finest level by an active set method. The latter allows several indices of the active set to be updated simultaneously. This reduces the computational effort significantly, when compared to standard active set methods that update one index at a time. Applications to image restoration are presented. Springer-Verlag, 2010 Constrained ill-posed problems nationallicence Nonnegativity nationallicence Active set method nationallicence Multilevel method nationallicence Image restoration nationallicence Morigi S. Department of Mathematics-CIRAM, University of Bologna, Piazza Porta S. Donato 5, 40126, Bologna, Italy aut Plemmons R. Departments of Mathematics and Computer Science, Wake Forest University, 27106, Winston Salem, NC, USA aut Reichel L. Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut Sgallari F. Department of Mathematics-CIRAM, University of Bologna, Via Saragozza 8, 40123, Bologna, Italy aut Calcolo Springer Milan 48/1(2011-03-01), 89-105 0008-0624 48:1<89 2011 48 10092 https://doi.org/10.1007/s10092-010-0030-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10092-010-0030-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Morigi S. Department of Mathematics-CIRAM, University of Bologna, Piazza Porta S. Donato 5, 40126, Bologna, Italy aut NATIONALLICENCE 700 1- Plemmons R. Departments of Mathematics and Computer Science, Wake Forest University, 27106, Winston Salem, NC, USA aut NATIONALLICENCE 700 1- Reichel L. Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut NATIONALLICENCE 700 1- Sgallari F. Department of Mathematics-CIRAM, University of Bologna, Via Saragozza 8, 40123, Bologna, Italy aut NATIONALLICENCE 773 0- Calcolo Springer Milan 48/1(2011-03-01), 89-105 0008-0624 48:1<89 2011 48 10092 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer