Past and future of inverse problems

Journal of Mathematical Physics

Volumn 41, Issue 6, 2000, Pages 4082-4124

  Sabatier, Pierre C ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034391428     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533336     Document Type: Review

References (237)

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96. See, in particular, M. M. Lavrentiev, Some Improperly Posed Problems of Mathematical Physics (Springer, Berlin, 1967); M. M. Lavrentiev, V. G. Romanov, and S. P. Shishatskii, III-Posed Problems in Mathematical Physics and Analysis (Nauka, Moscow, 1980); V. G. Romanov and S. I. Kabanikhin, Inverse Problems of Geoelectrics (Nauka, Moscow, 1991), and see Ref. 101.
97. See, in particular, M. M. Lavrentiev, Some Improperly Posed Problems of Mathematical Physics (Springer, Berlin, 1967); M. M. Lavrentiev, V. G. Romanov, and S. P. Shishatskii, III-Posed Problems in Mathematical Physics and Analysis (Nauka, Moscow, 1980); V. G. Romanov and S. I. Kabanikhin, Inverse Problems of Geoelectrics (Nauka, Moscow, 1991), and see Ref. 101.
98. See Ref. 6 and M. Z. Nashed (ed.), Generalised Inverses and Applications (Academic, New York, 1976); C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Pitman, Boston, 1984); A. N. Tikhonov and A. V. Goncharsky. III-Posed Problems in the Natural Sciences (Mir, Moscow, 1987): A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of III Posed Problems (Kluwer, Dordrecht, 1990).
99. See Ref. 6 and M. Z. Nashed (ed.), Generalised Inverses and Applications (Academic, New York, 1976); C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Pitman, Boston, 1984); A. N. Tikhonov and A. V. Goncharsky. III-Posed Problems in the Natural Sciences (Mir, Moscow, 1987): A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of III Posed Problems (Kluwer, Dordrecht, 1990).
100. See Ref. 6 and M. Z. Nashed (ed.), Generalised Inverses and Applications (Academic, New York, 1976); C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Pitman, Boston, 1984); A. N. Tikhonov and A. V. Goncharsky. III-Posed Problems in the Natural Sciences (Mir, Moscow, 1987): A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of III Posed Problems (Kluwer, Dordrecht, 1990).
101. See Ref. 6 and M. Z. Nashed (ed.), Generalised Inverses and Applications (Academic, New York, 1976); C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Pitman, Boston, 1984); A. N. Tikhonov and A. V. Goncharsky. III-Posed Problems in the Natural Sciences (Mir, Moscow, 1987): A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of III Posed Problems (Kluwer, Dordrecht, 1990).
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105. M. G. Romanov, Inverse Problems of Mathematical Physics (VNU, Utrecht, 1987); V. B. Glasko, Inverse Problems of Mathematical Physics (Ameican Institute of Physics, New York, 1984); M. M. Lavrentiev and L. Ya. Saveliev, Linear Operators and III-posed Problems (Consultants Bureau, New York, 1995): C. W. Groetsch, Inverse Problems in the Mathematical Sciences (Vieweg, Braunscheweig, 1993).
106. M. G. Romanov, Inverse Problems of Mathematical Physics (VNU, Utrecht, 1987); V. B. Glasko, Inverse Problems of Mathematical Physics (Ameican Institute of Physics, New York, 1984); M. M. Lavrentiev and L. Ya. Saveliev, Linear Operators and III-posed Problems (Consultants Bureau, New York, 1995): C. W. Groetsch, Inverse Problems in the Mathematical Sciences (Vieweg, Braunscheweig, 1993).
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110. See Refs. 59-61 and M. Hanke and P. C. Hansen, Surv. Math. Ind. 3, 253-315 (1993); H. W. Engl. M. Hanke, and A. Neubauer, Regularisation of Inverse Problems (Kluwer, Dordrecht, 1996).
111. C. R. Rao, Linear Statistical Inference and its Applications, 2nd ed. (Wiley, Chichester, 1973); J. V. Beck and K. J. Arnold, Parameter Estimation in Engineering and Science (Wiley, Chichester, 1977); A. I. Dale, A History of Inverse Probability (Springer, New York, 1991).
112. C. R. Rao, Linear Statistical Inference and its Applications, 2nd ed. (Wiley, Chichester, 1973); J. V. Beck and K. J. Arnold, Parameter Estimation in Engineering and Science (Wiley, Chichester, 1977); A. I. Dale, A History of Inverse Probability (Springer, New York, 1991).
113. C. R. Rao, Linear Statistical Inference and its Applications, 2nd ed. (Wiley, Chichester, 1973); J. V. Beck and K. J. Arnold, Parameter Estimation in Engineering and Science (Wiley, Chichester, 1977); A. I. Dale, A History of Inverse Probability (Springer, New York, 1991).
114. J. H. Justice (ed.), Maximum Entropy and Bayesian Methods in Applied Statistics (Cambridge U. P., Cambridge, 1986); J. A. Scales and R. Snieder, Geophysics 62, 1045-1046 (1998); B. G. Fitzpatrick, Inverse Probl. 7, 675-702 (1991).
115. J. H. Justice (ed.), Maximum Entropy and Bayesian Methods in Applied Statistics (Cambridge U. P., Cambridge, 1986); J. A. Scales and R. Snieder, Geophysics 62, 1045-1046 (1998); B. G. Fitzpatrick, Inverse Probl. 7, 675-702 (1991).
116. J. H. Justice (ed.), Maximum Entropy and Bayesian Methods in Applied Statistics (Cambridge U. P., Cambridge, 1986); J. A. Scales and R. Snieder, Geophysics 62, 1045-1046 (1998); B. G. Fitzpatrick, Inverse Probl. 7, 675-702 (1991).
117. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
118. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
119. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
120. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
121. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
122. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
123. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
124. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
125. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
126. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
127. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
128. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
129. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
130. For a multivariate sample, containing monographs and proceedings, and to be added to other references, see J. B. Bednar, R. Redner, E. Robinson, and A. Weglein (eds.), Conference on Inverse Scattering: Theory and Application (SIAM, Philadelphia, 1983); F. Santosa, Y. H. Pao, W. W. Symes, and C. Holland (eds.), Inverse Problems of Acoustic and Elastic waves (SIAM, Philadelphia, 1984); I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy (Hilger, Bristol, 1986); G. Talenti (ed.), Inverse Problems (Springer, Berlin, 1986); J. R. Cannon and U. Hornung (ed.), Inverse Problems (Birkhauser, Basel, 1986): M. Yamaguti, K. Hayakawa, Y. Iso, M. Mori, T. Nishida, K. Tomoeda, and M. Yamamoto (eds.), Inverse Problems in Engineering Sciences (Springer, Berlin, 1991); M. Bertero and E. R. Pike (eds.), Inverse Problems in Scattering and Imaging (Hilger, Bristol, 1992); J. Corones, G. Kristensson, P. Nelson, and D.L. Seth (eds.), Invariant Imbedding and Inverse Problems (SIAM, Philadelphia, 1992); H. D. Bui, Introduction aux problemes inverses en mecanique des materiaux (Eyrolles, Paris, 1993); H. Von Geramb (ed.), Quantum Inversion Theory and Applications (Springer, Berlin. 1994); N. Z. Sun. Inverse Problems in Groundwater Modeling (Kluwer Academic, Dordrecht, 1994): H. W. Engl and W. Rundell, (ed.), Inverse Problems in Diffusion Processes (SIAM. Philadelphia. 1995): S. He, V. Weston, and S. Ström, Time Domain Wave-Splittings and Inverse Problems (Oxford U. P., Oxford, 1998). See also the monographs published in the last few years in the series "Inverse and III posed Problems Series," VSP Utrecht.
131. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
132. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
133. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
134. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
135. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
136. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
137. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
138. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
139. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
140. "RCP 264" annual meetings (1972-1995): "Interdisciplinary Study of Inverse Problems," Proceedings edited by P. C. Sabatier in Applied Inverse Problems (Springer Verlag, Berlin, 1978); Problèmes inverses-évolution non linéaire (CNRS, 1980); Problèmes Inverses: Cahiers Mathématiques de Montpellier 24 (1981) 28 (1982) 31 (1983) 32 (1984) 35, (1985); Inverse Problems: An Interdisciplinary Study (Academic, New York, 1987); Some Topics on Inverse Problems (World Scientific, Singapore, 1988); Inverse Methods in Action (Springer Verlag, Berlin, 1989).
141. "RCP 264" annual meetings (1972-1995): "Interdisciplinary
142. A. Roger, IEEE Trans. Antennas Propag. AP-29, 232-238 (1981); Electromagnetics 2, 69-83 (1982).
143. A. Roger, IEEE Trans. Antennas Propag. AP-29, 232-238 (1981); Electromagnetics 2, 69-83 (1982).
144. R. E. Kleinman and P. M. Van den Berg, Radio Sci. 29, 1157-1169 (1994).
145. L. Souriau, B. Duchêne, D. Lesselier, and R. E. Kleinman, Inverse Probl. 12, 463-481 (1996).
146. B. Duchêne and D. Lesselier, IEEE Antennas Propag. Mag. 38, 45-47 (1996); K. Belkébir, J. M. Ellisalt, J. M. Geffrin, and Ch. Pichot, ibid. 38, 41-44 (1996); P. M. Van der Berg, E.. J. Kooij, and R. E. Kleinman, ibid. 39, 29-32 (1997).
147. B. Duchêne and D. Lesselier, IEEE Antennas Propag. Mag. 38, 45-47 (1996); K. Belkébir, J. M. Ellisalt, J. M. Geffrin, and Ch. Pichot, ibid. 38, 41-44 (1996); P. M. Van der Berg, E.. J. Kooij, and R. E. Kleinman, ibid. 39, 29-32 (1997).
148. B. Duchêne and D. Lesselier, IEEE Antennas Propag. Mag. 38, 45-47 (1996); K. Belkébir, J. M. Ellisalt, J. M. Geffrin, and Ch. Pichot, ibid. 38, 41-44 (1996); P. M. Van der Berg, E.. J. Kooij, and R. E. Kleinman, ibid. 39, 29-32 (1997).
149. T. E. Angell and R. E. Kleinman, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 44, 1246-1257 (1984); Ann. Telecommun. 40, 341-349 (1985); Math. Methods Appl. Sci. 8, 50-76 (1986); IMA J. Appl. Math. 47, 265-281 (1991); Proc. IEEE 79, 1559-1568 (1991).
150. T. E. Angell and R. E. Kleinman, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 44, 1246-1257 (1984); Ann. Telecommun. 40, 341-349 (1985); Math. Methods Appl. Sci. 8, 50-76 (1986); IMA J. Appl. Math. 47, 265-281 (1991); Proc. IEEE 79, 1559-1568 (1991).
151. T. E. Angell and R. E. Kleinman, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 44, 1246-1257 (1984); Ann. Telecommun. 40, 341-349 (1985); Math. Methods Appl. Sci. 8, 50-76 (1986); IMA J. Appl. Math. 47, 265-281 (1991); Proc. IEEE 79, 1559-1568 (1991).
152. T. E. Angell and R. E. Kleinman, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 44, 1246-1257 (1984); Ann. Telecommun. 40, 341-349 (1985); Math. Methods Appl. Sci. 8, 50-76 (1986); IMA J. Appl. Math. 47, 265-281 (1991); Proc. IEEE 79, 1559-1568 (1991).
153. T. E. Angell and R. E. Kleinman, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 44, 1246-1257 (1984); Ann. Telecommun. 40, 341-349 (1985); Math. Methods Appl. Sci. 8, 50-76 (1986); IMA J. Appl. Math. 47, 265-281 (1991); Proc. IEEE 79, 1559-1568 (1991).
154. M. Bath and A. J. Berkhout, Mathematical Aspects of Seismology (Geophysical, London, 1984); L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media (Springer, Berlin, 1992), Vois. I and II.
155. M. Bath and A. J. Berkhout, Mathematical Aspects of Seismology (Geophysical, London, 1984); L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media (Springer, Berlin, 1992), Vois. I and II.
156. "Special Section on Inverse Problems in Geophysics," in Inverse Probl. 14, 369-520 (1998); R. Cassinis (ed.), The Solution of the Inverse Problem in Geophysical Interpretation (Plenum, New York, 1980); R. L. Parker, Geophysical Inverse Theory (Princeton U. P., Princeton, NJ, 1994); A. Tarantola, Inverse Problem Theory: Methods for Fitting and Model Parameters Estimation (Elsevier, New York, 1987); W. Munk, P. Worcester, and C. Wunsch. Ocean Acoustic Tomography (Cambridge U.P., Cambridge, 1995).
157. "Special Section on Inverse Problems in Geophysics," in Inverse Probl. 14, 369-520 (1998); R. Cassinis (ed.), The Solution of the Inverse Problem in Geophysical Interpretation (Plenum, New York, 1980); R. L. Parker, Geophysical Inverse Theory (Princeton U. P., Princeton, NJ, 1994); A. Tarantola, Inverse Problem Theory: Methods for Fitting and Model Parameters Estimation (Elsevier, New York, 1987); W. Munk, P. Worcester, and C. Wunsch. Ocean Acoustic Tomography (Cambridge U.P., Cambridge, 1995).
158. "Special Section on Inverse Problems in Geophysics," in Inverse Probl. 14, 369-520 (1998); R. Cassinis (ed.), The Solution of the Inverse Problem in Geophysical Interpretation (Plenum, New York, 1980); R. L. Parker, Geophysical Inverse Theory (Princeton U. P., Princeton, NJ, 1994); A. Tarantola, Inverse Problem Theory: Methods for Fitting and Model Parameters Estimation (Elsevier, New York, 1987); W. Munk, P. Worcester, and C. Wunsch. Ocean Acoustic Tomography (Cambridge U.P., Cambridge, 1995).
159. "Special Section on Inverse Problems in Geophysics," in Inverse Probl. 14, 369-520 (1998); R. Cassinis (ed.), The Solution of the Inverse Problem in Geophysical Interpretation (Plenum, New York, 1980); R. L. Parker, Geophysical Inverse Theory (Princeton U. P., Princeton, NJ, 1994); A. Tarantola, Inverse Problem Theory: Methods for Fitting and Model Parameters Estimation (Elsevier, New York, 1987); W. Munk, P. Worcester, and C. Wunsch. Ocean Acoustic Tomography (Cambridge U.P., Cambridge, 1995).
160. "Special Section on Inverse Problems in Geophysics," in Inverse Probl. 14, 369-520 (1998); R. Cassinis (ed.), The Solution of the Inverse Problem in Geophysical Interpretation (Plenum, New York, 1980); R. L. Parker, Geophysical Inverse Theory (Princeton U. P., Princeton, NJ, 1994); A. Tarantola, Inverse Problem Theory: Methods for Fitting and Model Parameters Estimation (Elsevier, New York, 1987); W. Munk, P. Worcester, and C. Wunsch. Ocean Acoustic Tomography (Cambridge U.P., Cambridge, 1995).
161. G. Chavent, Adv. Water Resour. 14, 55-63 (1991); see also G. Chavent, in "Problèmes Inverses,"CEA EDF INRIA Publ. Paris (1990), pp. 1-12; W. W. Symes, ibid., pp. 33-123.
162. G. Chavent, Adv. Water Resour. 14, 55-63 (1991); see also G. Chavent, in "Problèmes Inverses,"CEA EDF INRIA Publ. Paris (1990), pp. 1-12; W. W. Symes, ibid., pp. 33-123.
163. G. Chavent, Adv. Water Resour. 14, 55-63 (1991); see also G. Chavent, in "Problèmes Inverses,"CEA EDF INRIA Publ. Paris (1990), pp. 1-12; W. W. Symes, ibid., pp. 33-123.
164. M. V. de Hoop and G. Spencer. Inverse Probl. 12, 219-239 (1996).
165. P. J. M. Van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Practice (Kluwer Academic, Dordrecht, 1992).
166. D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, MA, 1989); R. Cerf. "Une théorie asymptotique des algorithmes génétiques (synthèse)," Ph.D. Thesis, Montpellier technical report 94-04, 1994.
167. D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, MA, 1989); R. Cerf. "Une théorie asymptotique des algorithmes génétiques (synthèse)," Ph.D. Thesis, Montpellier technical report 94-04, 1994.
168. Y. Cherruault, Biomathématiques (Presses Universitaires de France, Paris, 1983).
169. G. Backus and F. Gilbert, Geophys. J. R. Astron. Soc. 13, 247-276 (1967); ibid. 16, 169-205 (1968); G. Backus, Proc. Natl. Acad. Sci. USA 65, 1-105, 281-287 (1970).
170. G. Backus and F. Gilbert, Geophys. J. R. Astron. Soc. 13, 247-276 (1967); ibid. 16, 169-205 (1968); G. Backus, Proc. Natl. Acad. Sci. USA 65, 1-105, 281-287 (1970).
171. G. Backus and F. Gilbert, Geophys. J. R. Astron. Soc. 13, 247-276 (1967); ibid. 16, 169-205 (1968); G. Backus, Proc. Natl. Acad. Sci. USA 65, 1-105, 281-287 (1970).
172. M. Bertero, C. de Mol, and E. R. Pike, Inverse Probl. 1, 301-330 (1985); ibid. 4, 573-594 (1988).
173. M. Bertero, C. de Mol, and E. R. Pike, Inverse Probl. 1, 301-330 (1985); ibid. 4, 573-594 (1988).
174. D. Slepian, SIAM Rev. 25, 379-393 (1983).
175. P. C. Sabatier, Lect. Notes Math. 1497, 187-194 (1991).
176. P. C. Sabatier, Proc. R. Soc, London, Ser. A 337, 68-70 (1974); P. C. Sabatier, Revue du Cétedhec. Ondes et Signal 76, 1-18 (1983).
177. P. C. Sabatier, Proc. R. Soc, London, Ser. A 337, 68-70 (1974); P. C. Sabatier, Revue du Cétedhec. Ondes et Signal 76, 1-18 (1983).
178. See Ref. 9 and R. N. Mc Donough, Detection of Signals in Noise, 2nd ed. (Academic, San Diego, 1995); H. Niemann, Pattern Analysis and Understanding, 2nd ed. (Springer, Berlin, 1990).
179. See Ref. 9 and R. N. Mc Donough, Detection of Signals in Noise, 2nd ed. (Academic, San Diego, 1995); H. Niemann, Pattern Analysis and Understanding, 2nd ed. (Springer, Berlin, 1990).
180. J. Serra and L. Vincent, Circuits Syst. Signal Process. 11, 47-108 (1992), H. J. A. M. Heijmans, SIAM Rev. 37, 1-36 (1995).
181. J. Serra and L. Vincent, Circuits Syst. Signal Process. 11, 47-108 (1992), H. J. A. M. Heijmans, SIAM Rev. 37, 1-36 (1995).
182. A. Grunbaum, in Ref. 67, Inverse Methods in Action, pp. 16-21.
183. M. Hamajlainen, R. Hari, R. J. Ilmoniensi, J. Knuutila, and O. V. Lenvasmaa, Rev. Mod. Phys. 65, 413-497 (1993).
184. The annual meetings PIERS (Progress in Electromagnetic Research Symposium) and URSI (Union of Radio Science International) all contain sessions on electromagnetic inverse problems. See also Ret. 66, in particular the last cited one and, for more specific examples of applications, the two sets in the NATO Series; W. Boerner (ed.), Inverse Methods in Electromagnetic Imaging, Parts I and II (Reidel, Dordrecht, 1985) and W. Boerner (ed.), "Direct and Inverse Methods in Radar Polarimetry, Parts I and II (Reidel, Dordrecht, 1992).
185. The annual meetings PIERS (Progress in Electromagnetic Research Symposium) and URSI (Union of Radio Science International) all contain sessions on electromagnetic inverse problems. See also Ret. 66, in particular the last cited one and, for more specific examples of applications, the two sets in the NATO Series; W. Boerner (ed.), Inverse Methods in Electromagnetic Imaging, Parts I and II (Reidel, Dordrecht, 1985) and W. Boerner (ed.), "Direct and Inverse Methods in Radar Polarimetry, Parts I and II (Reidel, Dordrecht, 1992).
186. A. Litman and D. Lesselier, Inverse Probl. 15, 99-111 (1999). See also J. P. Kaipio, V. Kolehmainen, M. Vankhonen, and E. Somersalo, Inverse Prob. 15, 713-729 (1999).
187. A. Litman and D. Lesselier, Inverse Probl. 15, 99-111 (1999). See also J. P. Kaipio, V. Kolehmainen, M. Vankhonen, and E. Somersalo, Inverse Prob. 15, 713-729 (1999).
188. E. Haber and D. Oldenburg, Inverse Probl. 13, 63-77 (1997).
189. Let me cite the only analysis I have fully participated in: S. Rzadkiewicz, P. Heinrich, P. C. Sabatier, B. Savoye, and J. F. Bourillet, "Numerical modelling of a landslide-generated tsunami: the 1979 Nice event." Report of departement des sciences de l'environnement, CEA, Bruyères le Chatel to be published in Pure Appl. Geophys.
190. P. C. Sabatier, Inverse Probl. 11, 1233-1245 (1995); in Inverse Problems in Geophysical Applications, edited by H. Engl, W. Rundell, D. Colton, and A. Louis (SIAM, Philadelphia, 1997), pp. 27-42.
191. P. C. Sabatier, Inverse Probl. 11, 1233-1245 (1995); in Inverse Problems in Geophysical Applications, edited by H. Engl, W. Rundell, D. Colton, and A. Louis (SIAM, Philadelphia, 1997), pp. 27-42.
192. R. Snieder, in Diffuse Waves in Complex Media, edited by J. P. Fouque (Kluwer Academic, Dordrecht, 1999), pp. 405-454; J. Scales and R. Snieder, Geophysics 62, 1355-1358 (1997).
193. R. Snieder, in Diffuse Waves in Complex Media, edited by J. P. Fouque (Kluwer Academic, Dordrecht, 1999), pp. 405-454; J. Scales and R. Snieder, Geophysics 62, 1355-1358 (1997).
194. P. Courtier and O. Talagrand, Tellus 42A, 531-549 (1990).
195. P. C. Sabatier, "Elbow scattering and inverse scattering applications to LKdV and KdV," J. Math. Phys. 41, 414-436 (2000).
196. A. S. Fokas and B. Pelloni, Proc. R. Soc. London, Ser. A 454, 645-657; and to be published.
197. F. Calogero and A. Degasperis, Spectral Transform and Solitons (North Holland, Amsterdam, 1982); M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolutions Equations and Inverse Scattering (Cambridge U. P., Cambridge 1991); see also the almost annual proceedings of the meeting "Needs" (Nonlinear Evolution Equations and Dynamical Systems), existing since 1980 (World Scientific, Singapore), and A. S. Fokas, J. Math. Phys. 41, 4188 (2000).
198. F. Calogero and A. Degasperis, Spectral Transform and Solitons (North Holland, Amsterdam, 1982); M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolutions Equations and Inverse Scattering (Cambridge U. P., Cambridge 1991); see also the almost annual proceedings of the meeting "Needs" (Nonlinear Evolution Equations and Dynamical Systems), existing since 1980 (World Scientific, Singapore), and A. S. Fokas, J. Math. Phys. 41, 4188 (2000).
199. F. Calogero and A. Degasperis, Spectral Transform and Solitons (North Holland, Amsterdam, 1982); M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolutions Equations and Inverse Scattering (Cambridge U. P., Cambridge 1991); see also the almost annual proceedings of the meeting "Needs" (Nonlinear Evolution Equations and Dynamical Systems), existing since 1980 (World Scientific, Singapore), and A. S. Fokas, J. Math. Phys. 41, 4188 (2000).
200. F. Calogero and A. Degasperis, Spectral Transform and Solitons (North Holland, Amsterdam, 1982); M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolutions Equations and Inverse Scattering (Cambridge U. P., Cambridge 1991); see also the almost annual proceedings of the meeting "Needs" (Nonlinear Evolution Equations and Dynamical Systems), existing since 1980 (World Scientific, Singapore), and A. S. Fokas, J. Math. Phys. 41, 4188 (2000).
201. A. S. Fokas and M. J. Ablowitz, Phys. Rev Lett. 47, 1096-1100 (1981); P. C. Sabatier, in Nonlinear Evolution Equations and Dynamical Systems, edited by V. Makhankov, A. Bishop, and D. Holm (World Scientific, Singapore, 1995), pp. 208-222.
202. A. S. Fokas and M. J. Ablowitz, Phys. Rev Lett. 47, 1096-1100 (1981); P. C. Sabatier, in Nonlinear Evolution Equations and Dynamical Systems, edited by V. Makhankov, A. Bishop, and D. Holm (World Scientific, Singapore, 1995), pp. 208-222.
203. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer Verlag, Berlin, 1991); see also Beals et al. in Ref. 37 and P. C. Sabatier in Inverse Problems, edited by J. R. Cannon and U. Homung (Birkhäuser, Basel, 1986), pp. 185-191.
204. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer Verlag, Berlin, 1991); see also Beals et al. in Ref. 37 and P. C. Sabatier in Inverse Problems, edited by J. R. Cannon and U. Homung (Birkhäuser, Basel, 1986), pp. 185-191.
205. B. Zachariev and M. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer, Berlin, 1990): B. Zachariev and V. M. Chabanov, Inverse Probl. 13, R47-R78 (1998).
206. B. Zachariev and M. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer, Berlin, 1990): B. Zachariev and V. M. Chabanov, Inverse Probl. 13, R47-R78 (1998).
207. H. J. Krappe and R. Lipperheide (eds), Advanced Methods in the Evaluation of Nuclear Scattering Data (Springer, Berlin, 1985);
208. b P. C. Sabatier, in Proc. Ann. GAMM Meeting, Regensburg (1997).
209. J. D. Achenbach, A. K. Gautesen, and H. Mc Maken, Ray Methods for Waves in Elastic Solids (Pitman, London, 1982).
210. A. J. Devaney, Opt. Lett. 6, 374-376 (1981); D. Pommet, M. A. Fiddy et al., in Experimental and Numerical Methods for Solving Ill-posed Inverse Problems: Medical and Non Medical Applications, edited by R. L. Barbour, M. J. Carvlin, and M. A. Fiddy, SPIE Proc. Series. Vol. 2570, (1995), pp. 38-48.
211. A. J. Devaney, Opt. Lett. 6, 374-376 (1981); D. Pommet, M. A. Fiddy et al., in Experimental and Numerical Methods for Solving Ill-posed Inverse Problems: Medical and Non Medical Applications, edited by R. L. Barbour, M. J. Carvlin, and M. A. Fiddy, SPIE Proc. Series. Vol. 2570, (1995), pp. 38-48.
212. A. J. Devaney, Inverse Probl. 5, 501-521 (1989).
213. P. C. Sabatier, Ref. 102a, pp. 1-19.
214. M. A. Brodski, Geophys, J. R. Astron. Soc. 66, 727-732 (1981); SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 46, 345-350 (1986); M. A. Brodski and E. Panakhov, Inverse Probl. 6, 320-330 (1990).
215. M. A. Brodski, Geophys, J. R. Astron. Soc. 66, 727-732 (1981); SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 46, 345-350 (1986); M. A. Brodski and E. Panakhov, Inverse Probl. 6, 320-330 (1990).
216. M. A. Brodski, Geophys, J. R. Astron. Soc. 66, 727-732 (1981); SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 46, 345-350 (1986); M. A. Brodski and E. Panakhov, Inverse Probl. 6, 320-330 (1990).
217. D. Zidarov, Inverse Gravimetric Problem in Geoprospecting and Geodesy (Elsevier, Amsterdam, 1990); R. Barzaghi and F. Sanso, Inverse Probl. 14, 499-520 (1998).
218. D. Zidarov, Inverse Gravimetric Problem in Geoprospecting and Geodesy (Elsevier, Amsterdam, 1990); R. Barzaghi and F. Sanso, Inverse Probl. 14, 499-520 (1998).
219. See Ref. 11 and P. C. Sabatier, Geophys. J. R. Astron. Soc. 48, 443-469 (1977); V. Richard, R. Bayer, and M. Cuer, Geophysics 42, 1215-1229 (1984); P. C. Sabatier, in Inverse and Ill-Posed Problems, edited by H. W. Engl and C. W. Groetsch (Academic, Boston, 1987); V. Richard, Ph.D. thesis, Montpellier, 1983.
220. See Ref. 11 and P. C. Sabatier, Geophys. J. R. Astron. Soc. 48, 443-469 (1977); V. Richard, R. Bayer, and M. Cuer, Geophysics 42, 1215-1229 (1984); P. C. Sabatier, in Inverse and Ill-Posed Problems, edited by H. W. Engl and C. W. Groetsch (Academic, Boston, 1987); V. Richard, Ph.D. thesis, Montpellier, 1983.
221. See Ref. 11 and P. C. Sabatier, Geophys. J. R. Astron. Soc. 48, 443-469 (1977); V. Richard, R. Bayer, and M. Cuer, Geophysics 42, 1215-1229 (1984); P. C. Sabatier, in Inverse and Ill-Posed Problems, edited by H. W. Engl and C. W. Groetsch (Academic, Boston, 1987); V. Richard, Ph.D. thesis, Montpellier, 1983.
222. See Ref. 11 and P. C. Sabatier, Geophys. J. R. Astron. Soc. 48, 443-469 (1977); V. Richard, R. Bayer, and M. Cuer, Geophysics 42, 1215-1229 (1984); P. C. Sabatier, in Inverse and Ill-Posed Problems, edited by H. W. Engl and C. W. Groetsch (Academic, Boston, 1987); V. Richard, Ph.D. thesis, Montpellier, 1983.
223. A. R. Osborne, in Nonlinear Topics in Ocean Physics, edited by A. R. Osborne (North Holland, Amsterdam, 1991), pp. 669-698.
224. C. de Mol, The Superresolving Scanning Microscope: State of the Art, Université libre de Bruxelles (January 1992); M. Bertero, "Super-resolution by data inversion" Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1996), Vol. 36, pp. 129-178. That "superresolution" is always limited in any realistic model of measurements should not prevent seeking it; but physical methods which do not rely on waves, e.g., near field microscopes, may allow better results. Notice also that closely related problems, for instance the continuation of Earth Fields, were studied early in geodesy and geophysics - see for instance V. Courtillot, J. Ducruix, and J. L. Le Mouel, Lecture Notes in Physics 85, 48-83 (1978).
225. C. de Mol, The Superresolving Scanning Microscope: State of the Art, Université libre de Bruxelles (January 1992); M. Bertero, "Super-resolution by data inversion" Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1996), Vol. 36, pp. 129-178. That "superresolution" is always limited in any realistic model of measurements should not prevent seeking it; but physical methods which do not rely on waves, e.g., near field microscopes, may allow better results. Notice also that closely related problems, for instance the continuation of Earth Fields, were studied early in geodesy and geophysics - see for instance V. Courtillot, J. Ducruix, and J. L. Le Mouel, Lecture Notes in Physics 85, 48-83 (1978).
226. C. de Mol, The Superresolving Scanning Microscope: State of the Art, Université libre de Bruxelles (January 1992); M. Bertero, "Super-resolution by data inversion" Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1996), Vol. 36, pp. 129-178. That "superresolution" is always limited in any realistic model of measurements should not prevent seeking it; but physical methods which do not rely on waves, e.g., near field microscopes, may allow better results. Notice also that closely related problems, for instance the continuation of Earth Fields, were studied early in geodesy and geophysics - see for instance V. Courtillot, J. Ducruix, and J. L. Le Mouel, Lecture Notes in Physics 85, 48-83 (1978).
227. F. Calogero, in "What is Integrability?" edited by V. E. Zakharov (Springer Verlag, Berlin, 1991), pp. 1-61; F. Calogero and P. C. Sabatier, in Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, edited by M. Ablowitz, B. Fuchsteiner, and M. Kruskal (World Scientific, Singapore, 1987), pp. 251-269.
228. F. Calogero, in "What is Integrability?" edited by V. E. Zakharov (Springer Verlag, Berlin, 1991), pp. 1-61; F. Calogero and P. C. Sabatier, in Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, edited by M. Ablowitz, B. Fuchsteiner, and M. Kruskal (World Scientific, Singapore, 1987), pp. 251-269.
229. As an example of the interaction between theory and practice in inverse problems, see for example, the special section of Inverse Probl. 13, 555-606 (1997).
230. A. Grünbaum, CRM Proceedings Lecture Notes 14, Amer. Math. Soc. Providence (1998); Yu. Yu. Berest and A. P. Veselov, Russian Math. Surveys 49, 5-77 (1994); A. Grünbaum and L. Haine, Comm. Math. Phys. 184, 173-202 (1997).
231. A. Grünbaum, CRM Proceedings Lecture Notes 14, Amer. Math. Soc. Providence (1998); Yu. Yu. Berest and A. P. Veselov, Russian Math. Surveys 49, 5-77 (1994); A. Grünbaum and L. Haine, Comm. Math. Phys. 184, 173-202 (1997).
232. A. Grünbaum, CRM Proceedings Lecture Notes 14, Amer. Math. Soc. Providence (1998); Yu. Yu. Berest and A. P. Veselov, Russian Math. Surveys 49, 5-77 (1994); A. Grünbaum and L. Haine, Comm. Math. Phys. 184, 173-202 (1997).
233. "Inverse Problems," an international journal on the theory and practice of inverse problems, inverse methods and computerized inversion of data (first issue in February 1985), Institute of Physics Publ. ISSN: 0266-5611.
234. The three large size surveys we find in two recent issues of "Inverse Problems" are on "optical tomography in medical imaging," "industrial real world inverse problems (with exemplification based on the molecular weight distribution problem)" (April 1999), and "the inverse problem that arises in financial markets" (June 1999).
235. The three large size surveys we find in two recent issues of "Inverse Problems" are on "optical tomography in medical imaging," "industrial real world inverse problems (with exemplification based on the molecular weight distribution problem)" (April 1999), and "the inverse problem that arises in financial markets" (June 1999).
236. The three large size surveys we find in two recent issues of "Inverse Problems" are on "optical tomography in medical imaging," "industrial real world inverse problems (with exemplification based on the molecular weight distribution problem)" (April 1999), and "the inverse problem that arises in financial markets" (June 1999).
237. R. G. Newton, SIAM Rev. 12, 346-356 (1970).