caa a22 4500 378866540 CHVBK 20180305123359.0 cr unu---uuuuu 161128e20030901xx s 000 0 eng 10.1515/156939403769237079 doi (NATIONALLICENCE)gruyter-10.1515/156939403769237079 The problems of linear and quadratic programming for ill-posed problems on some compact sets [Elektronische Daten] [V. N. Titarenko, A. G. Yagola] In this paper the problem of finding the error of an approximate solution for ill-posed problems on some compact sets is discussed. Sets of bounded monotonic or convex functions and sets of functions with a given Lipschitz constant are considered. These functions are given on a segment. Two approaches are used to construct sets of approximate solutions. In the first approach we assume that a function for the right-hand side of an operator equation is given on the whole segment. In the second approach we use only grid values of this function. Applying these approaches, we obtain quadratic or linear programming problems and find functions bounding above and below these approximate solutions. In the paper we use two algorithms to find errors that determine the sets of approximate solutions for the cases when operators of the problems are positive or integral. The inverse problem for the heat conduction equation is considered as a model example. Copyright 2003, Walter de Gruyter Titarenko V. N. Department of Mathematics, Faculty of Physics, Moscow State University, Vorobyevy Gory, 119899 Moscow, Russia. E-mail: ill-posed@mail.ru, yagola@inverse.phys.msu.su aut Yagola A. G. Department of Mathematics, Faculty of Physics, Moscow State University, Vorobyevy Gory, 119899 Moscow, Russia. E-mail: ill-posed@mail.ru, yagola@inverse.phys.msu.su aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 311-328 0928-0219 11:3<311 2003 11 jiip https://doi.org/10.1515/156939403769237079 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403769237079 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Titarenko V. N. Department of Mathematics, Faculty of Physics, Moscow State University, Vorobyevy Gory, 119899 Moscow, Russia. E-mail: ill-posed@mail.ru, yagola@inverse.phys.msu.su aut NATIONALLICENCE 700 1- Yagola A. G. Department of Mathematics, Faculty of Physics, Moscow State University, Vorobyevy Gory, 119899 Moscow, Russia. E-mail: ill-posed@mail.ru, yagola@inverse.phys.msu.su aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 311-328 0928-0219 11:3<311 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter