Vol. 3, issue 06, article # 10

Kavkyanov S. I., Strepetova S. V. On taking into account the range of the solution when inverting an equation of the convolution type. // Atmospheric and oceanic optics. 1990. V. 3. No. 06. P. 574-579.    PDF
Copy the reference to clipboard

Abstract:

Regularized algorithms for solving numerically an integral equation of the convolution type that permit taking into account, together with the usually employed a priori information about the smoothness of the reconstructed function, data on the range of the function are studied. The effect of taking data of this type into account on the quality of reconstruction is studied in a numerical experiment. An iteration algorithm for reconstructing positive-definite functions is proposed and methods for adaptation under conditions of a priori uncertainty are examined.

References:

1. A.N. Tikhonov and V.Ya. Arsenin, Methods for Solving Improperly Posed Problems [in Russianl, Nauka, Moscow (1986), 287 pp.
2. V.F. Turchin and L.S. Turovtseva, Opt. Spektrosk 36, No. 2, 280–287 (1974).
3. S.I. Kavkyanov and G.M. Krekov, in: Abstracts of Reports at the 2nd Conference on Atmospheric Optics, Institute of Atmospheric Optics, Siberian Branch of the USSR Academy of Sciences, Tomsk (1980), Part 2, pp. 24–27.
4. Yu.G. Evtushenko, Methods for Solving Extremal Problems and their Applications to Optimization Systems [in Russian], Nauka, Moscow (1982), 260 pp.
5. S.I. Kavkynov and S.V. Strepetova, Opt . Atmos. 1, No. 6, 50–56 (1988).
6. G.I. Vasilenko, Theory of Signal Recovery [in Russian], Sov. Radio, Moscow (1979), 272 pp.
7. I.M. Amiantov, Selected Problems in Statistical Communication Theory [in Russian], Sov. Radio, Moscow (1971), 416 pp.