Applied Nonlinear Ill-Posed Problems and the Variational Approach for Constructing of Regularizing Algorithms

作者: I. V. Kochikov , G. M. Kuramshina , A. G. Yagola

DOI: 10.1007/978-1-4020-7975-7_13

关键词: Applied scienceInverse problemAlgorithmForce field (chemistry)Well-posed problemElectronic microscopyNonlinear system

摘要: At present, the theory of ill-posed problems is widely used to solve inverse problems in optics, spectroscopy, astrophysics, geophysics, plasma diagnostics, electronic microscopy, and …

参考文章(8)
A. B Bakushinskiĭ, A. Goncharsky, Ill-Posed Problems: Theory and Applications ,(1994)
A. S. Leonov, A. N. Tikhonov, A. G. Yagola, Nonlinear ill-posed problems ,(1997)
G. M. Kuramshina, F. Weinhold, I. V. Kochikov, A. G. Yagola, Yu. A. Pentin, Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov’s method of regularization Journal of Chemical Physics. ,vol. 100, pp. 1414- 1424 ,(1994) , 10.1063/1.466619
A.S. Leonov, Choice of regularization parameter for non-linear ill-posed problems with approximately specified operator USSR Computational Mathematics and Mathematical Physics. ,vol. 19, pp. 1- 15 ,(1979) , 10.1016/0041-5553(79)90032-6
G. M. Kuramshina, A. G. Yagola, A PRIORI CONSTRAINTS IN THE FORCE FIELD CALCULATIONS OF POLYATOMIC MOLECULES Journal of Structural Chemistry. ,vol. 38, pp. 181- 194 ,(1997) , 10.1007/BF02762644
I.V. Kochikov, G.M. Kuramshina, A.G. Yagola, Stable numerical methods of solving certain inverse problems of vibrational spectroscopy Ussr Computational Mathematics and Mathematical Physics. ,vol. 27, pp. 33- 40 ,(1989) , 10.1016/0041-5553(87)90187-X
A.S. Leonov, A.G. Yagola, Tikhonov's approach for constructing regularizing algorithms Ill-posed problems in natural sciences: Proceedings of the International Conference/eds. A.N.Tikhonov et al. pp. 71- 73 ,(1992)
A.S. Leonov, A.G. Yagola, Can ill-posed problem be solved if the data error is unknown Moscow University Physics Bulletin. ,vol. 50, pp. 25- 28 ,(1995)