an:00745882
Zbl 0817.65139
Golichev, I. I.
Iterative methods of solving ill-posed boundary-value problems
EN
Comput. Math. Math. Phys. 33, No. 11, 1427-1436 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 11, 1626-1637 (1993).
00025580
1993
j
65Z05 65N12 35R25 35J25
Tikhonov's method; minimization; quadratic functional; Cauchy problem; elliptic equations; ill-posed boundary-value problems; iterative regularization; convergence
Summary: Minimization of a quadratic functional with control at the boundary and observation on a certain surface is studied. The Cauchy problem for elliptic equations and other ill-posed boundary-value problems is considered as a special case. An iterative procedure is obtained for solving the problem by means of iterative regularization, the iterational parameters being found explicitly. The convergence of the process is accelerated by making use of the specific features of the given functional.