Abstract
In this chapter, we consider the equation
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Castro, A., Neuberger, J.W. A local inversion principle of the Nash-Moser type. SIAM J. Math. Anal., 33 (2001), 989–993.
Cheng, J., Yamamoto, M. One new strategy for a-priori choice of regularizing parameters in Tikhonov’s regularization Inverse Problems, 16 (2000), L31–L38.
Djatlov, G. Stability of an inverse problem for the Helmholtz equation. Sib. Math. J., 35 (1994), 583–601.
Ekeland, I., Temam, R. Convex Analysis and Variational Problems. North-Holland, 1976.
Engl, H.W., Hanke, M., Neubauer, A. Regularization of Inverse Problems. Kluwer, Dordrecht, 1996.
Hadamard, J. Lectures on Cauchy’s problem in linear partial differential equations. Dover, New York, 1953.
Hamilton, R. The inverse function theorem of Nash and Moser. Bull. AMS, 7 (1982), 65–222.
Hohage, T. Logarithmic convergence rates of the iteratively regularized Gauss-Newton Method for an inverse potential and inverse scattering problem. Inverse Problems, 13 (1997), 1279–1299.
Hörmander, L. The Analysis of Linear Partial Differential Operators. Springer Verlag, New York, 1983–1985.
Isakov, V. Inverse Source Problems. Math. Surveys and Monographs Series, Vol. 34, AMS, Providence, R.I., 1990.
Ivanov, V.K., Vasin, V.V., Tanana, V.P. Theory of linear ill-posed problems and its applications. Nauka, Moscow, 1978.
Maslov, V.P. The existence of a solution to an ill-posed problem is equivalent to the convergence of a regularization process. Uspekhi Mat. Nauk, 23 (1968), 183–184.
Tikhonov, A.N., Arsenin, V.Ya. Solutions of ill-posed problems. Transl. from Russian, John Wiley & Sons, New York - Toronto, 1977.
Yosida, K. Functional Analysis. Springer, 1980.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Isakov, V. (2017). Ill-Posed Problems and Regularization. In: Inverse Problems for Partial Differential Equations. Applied Mathematical Sciences, vol 127 . Springer, Cham. https://doi.org/10.1007/978-3-319-51658-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-51658-5_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51657-8
Online ISBN: 978-3-319-51658-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)