caa a22 4500 465821170 CHVBK 20180323112136.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF01931661 doi (NATIONALLICENCE)springer-10.1007/BF01931661 Eldén Lars Department of Mathematics, Linköping University, S-581 83, Linköping, Sweden aut Algorithms for the computation of functionals defined on the solution of a discrete ill-posed problem [Elektronische Daten] [Lars Eldén] We study a linear, discrete ill-posed problem, by which we mean a very ill-conditioned linear least squares problem. In particular we consider the case when one is primarily interested in computing a functional defined on the solution rather than the solution itself. In order to alleviate the ill-conditioning we require the norm of the solution to be smaller than a given constant. Thus we are lead to minimizing a linear functional subject to two quadratic constraints. We study existence and uniqueness for this problem and show that it is essentially equivalent to a least squares problem with a linear and a quadratic constraint, which is easier to handle computationally. Efficient algorithms are suggested for this problem. BIT Foundations, 1990 ill-posed nationallicence least squares nationallicence constraint nationallicence functional nationallicence algorithm nationallicence BIT Numerical Mathematics Kluwer Academic Publishers 30/3(1990-09-01), 466-483 0006-3835 30:3<466 1990 30 10543 https://doi.org/10.1007/BF01931661 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01931661 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Eldén Lars Department of Mathematics, Linköping University, S-581 83, Linköping, Sweden aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Kluwer Academic Publishers 30/3(1990-09-01), 466-483 0006-3835 30:3<466 1990 30 10543 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer