Direct methods of minimization in the problem of estimating the measure of incompatibility of operator equations. (English. Russian original) Zbl 0841.65040

Levin, A. M.; Filatova, G. B.

Comput. Math. Math. Phys. 35, No. 2, 227-235 (1995); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 2, 282-293 (1995).

Summary: The use of direct gradient algorithms of minimization in the method of the least estimate of a discrepancy used to regularize computations of the measure of incompatibility of operator equations of the first kind is investigated. Computer results of the use of the method are given.

MSC:

65J10	Numerical solutions to equations with linear operators
65J20	Numerical solutions of ill-posed problems in abstract spaces; regularization
47A50	Equations and inequalities involving linear operators, with vector unknowns

Keywords:

regularization algorithm; ill-posed problems; Hilbert spaces; direct gradient algorithms; method of the least estimate; measure of incompatibility; operator equations of the first kind