反问题参考书目

References - books

1.R. Kress, Linear Integral Equations, Springer-Verlag, New York,199

2.

2. A. N. Tikhonov, V. Y. Arsenin, On the solution of ill-posed problems, John

Wiley and Sons, New York, 1977.

3.H. W. Engl, E. Hanke and A. Neubauer, Regularization of inverse problem,

Kluwer, Dordrecht, 1996.

4. C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm

Equations of the First Kind, Pitman, Boston, 1984.

5. C. W. Groetsch, Inverse problem in the Mathematical Sciences, Vieweg,

Braunschweig, 1993.

6.V. A. Morozov, Regularization Methods for Ill-Posed Problems, CRC

Press,1993.

7. A. N. Tikhonov, A. S. Leonov and A. G. Yagola, Nonlinear ill-posed

problems, London , New York: Chapman & Hall, 1998.

8.O. M. Alifanov, Inverse Heat Transfer Problems, Springer Verlag, 1994.

9. A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problem,

Springer, 1996.

10.C. Susanne, L. Brenner, S. Ridgway, The mathematical Theory of Finite

Element Methods, Springer-Verlag, New York, 1994.

11.苏超伟，《偏微分方程逆问题的数值方法及其应用》，

12.M. A. Golberg, C. S. Chen, Discrete Projection Methods for Integral

Equations, Computational Mechanics Publications, Southampton, 1997

13.V. Isakov, Inverse Problems for Partial differential Equations,

Springer-Verlag, New York, 1998.

14.J. R. Cannon, The one-dimensional heat equation, Addison-Wesley Publishing

Company, 1984.

15.R. A. Adams, Sobolev spaces, Pure and Applied Mathematics, V ol. 65.

Academic Press, New York-London,1975.

16. D. V. Widder, The heat equation, Academic Press, 1975.

17.J. V. Beck, K. D. Cole, A. Haji-Sheikh, B. Litouhi, Heat conduction using

Green’s functions, Hemisphere Publishing Corporation, 1992.

18.D. Colton, Inverse acoustic and electromagnetic scattering theory,

Springer-Verlag, 1992.

19.D. L. Colton, Solution of boundary value problems by the methods of integral

operators, Pitman Publishing, 1976.

20.V. Isakov, Inverse Source Problem, AMS Providence, R. I., 1990.

21.A. L. Bukhgeim, Introduction to the theory of inverse problem, VSP, 2000.

22.G. Wahba, Spline models for observational data, Society for Industrial and

Applied Mathematics, 1990.

23.C. S. Chen, Y. C. Hon and R. A. Schaback, Scientific Computing with Radial

Basis Functions, preprint.

24.J.W. Thomas, Numerical partical Differential equations (Finite difference

methods), Springer,1995.

25.C. W. Groetsh, Inverse problem activities for undergraduates, 翻译版，程晋，

谭永基，刘继军。

26.R. Schaback, Reconstruction of Multivariate Functions form Scattered Data,

1997, preprint.

27.Jie Shen, Lecture notes on spectral methods, preprint.

28.M. J. D. Powell, The Theory of Radial Basis Function Approximation in 1990,

preprint.

29.Robert Dautray, Jacques-Louis Lions, Mathematical Analysis and Numerical

Methods For Science and Technology.

Volume 1: Physical Origins and Classical Methods

Volume 2: Function and Variational Methods

Volume 3: Spectral Theory and Applications.

Volume 4:Integral Equations and Numerical Methods.