Abstract
In addition to model building, as we did in the earlier chapters, we care very much about fitting observations, i.e., indirect measurements, to models. This is at the core of remote sensing, temperature retrieval, prospecting for oil, medical diagnosis, and other inverse problems. In this chapter we present several methods for the systematic formulation of inverse problems, and we give explicit computational procedures for carrying them out. We study their effectiveness and their robustness with respect to errors in observations, in models, in initial estimates. We present results of numerous computational experiments. Studies such as these serve in the planning of experiments. The benefits of analysis in the planning stages of a project can help to avoid unfruitful experiments and inferior designs.
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References
H. Kagiwada, System Identification: Methods and Applications, Addison-Wesley Publishing Company, Reading, Mass., 1974.
A. P. Wang and S. Ueno, “Invariant Imbedding and Inverse Problems with Applications to Radiative Transfer,” to appear in Computer Math. Applic.
R. Bellman Dynamic Programming, Princeton University Press, Princeton, 1959.
R. Kalaba, “On Nonlinear Differential Equations, the Maximum Operation, and Monotone Convergence,” J. Math. and Mech., 1959, pp. 519–574.
R. Bellman, H. Kagiwada, and R. Kalaba, “Orbit Determination as a Multi-Point Boundary-Value Problem,” Proc. National Academy of Sciences, Vol. 48, 1962, pp. 1327–1329.
R. Bellman, H. Kagiwada, R. Kalaba, and S. Ueno, “Inverse Problems in Radiative Transfer: Layered Media,” Icarus, Vol. 4, 1965, pp. 119–126.
T. Kohonen, Self-Organization and Associative Memory, Springer-Verlag, New York, 1987.
H. Kagiwada, R. Kalaba, S. Timko, and S. Ueno, “Associative Memories for System Identification: Inverse Problems in Remote Sensing,” Mathematical and Computational Modelling, Vol. 14, 1990, pp. 200–202.
D. Marr and T. Poggio, “A Computational Theory of Human Stero Vision,” Proceedings of the Royal Society London, Series B204, 1979, pp. 301–328.
W. Press, et al., Numerical Recipes in C, Cambridge University Press, Cambridge, 1992.
R. E. Wengert, “A Simple Automatic Derivative Evaluation Program,” Communications of the Assoc. for Computing Machinery, Vol. 7, 1964, pp. 463–464.
R. Bellman, H. Kagiwada and R. Kalaba, “Wengert’s Numerical Method for Partial Derivatives, Orbit Determination, and Quasilinearization,” Comm. Assoc. Comput. Mach., Vol. 8, 1965, pp. 231–232.
H. Kagiwada, R. Kalaba, N. Rasakhoo, and K. Spingarn, Numerical Derivatives and Nonlinear Analysis, Plenum Press, New York, 1986.
R. W. Hamming, Numerical Methods for Scientists and Engineers, Dover Publications, New York, 1973.
R. Bellman, H. Kagiwada and R. Kalaba, “Numerical Inversion of Laplace Transforms and Some Inverse Problems in Radiative Transfer,” J. Atmosph. Sci., Vol. 23, 1966, pp. 555–559.
H. H. Kagiwada, J. K. Kagiwada and R. E. Kalaba, “Precision Passive Ranging,” Comput and Math. with Appl., Vol. 26, 1993, pp. 89–96.
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© 1998 Springer-Verlag Tokyo
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Natsuyama, H.H., Ueno, S., Wang, A.P. (1998). Inverse Problems. In: Terrestrial Radiative Transfer. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68527-2_3
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DOI: https://doi.org/10.1007/978-4-431-68527-2_3
Publisher Name: Springer, Tokyo
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