Analytic solution of ill-posed problems via dynamic methods
AbstractThe inverse problems of continuous differential and integral equations approximation with finite discrete algebraic systems and the problems of local linearization of nonlinear equations by the provided information are reduced to solving the linear algebraic systems. Matrices of such systems are usually ill-conditioned due to ill-posed problems according to Hadamard correctness. As a solution to these problems a dynamical method for regularization was proposed . In order to reduce the computation time of the algorithm, a second order modification of the dynamical method is proposed. This paper provides mathematical tools based on this method. A practical example shows its effectiveness.
Tikhonov А.N., Аrsenin V.YA. Metody resheniya nekorrektnykh zadach. — M.: Nauka, 1979. — 284 s.
Forsayt Dzh., Mal’kol’m M., Mouler K. Mashinnyye metody matematicheskikh vychisleniy: Per. s angl. Ikramova KH.D. — M.: Mir, 1980. — 277 s.
Gutenmakher L.I., Timoshenko YU.А., Tikhonchuk S.T. O dinamicheskom metode resheniya nekorrektnykh zadach // Dokl. АN SSSR. — 1977. — 237. — № 4. — S. 776–778.
Vasil’yeva А.B., Tikhonov А.N. Integral’nyye uravneniya. — M: Fizmatlit, 2002. — 158 s.