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Choice of regularization parameter in solving incorrect problems

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Literature Cited

  1. V. I. Iveronova, A. N. Tikhonov, P. N. Zaikin, and A. P. Zvyagina, “Determination of the phonon spectrum of crystals on the basis of heat capacity,” Fiz. Tverd. Tela,8, No. 12, 3459–3462 (1966).

    Google Scholar 

  2. A. I. Tikhonov, “On the solution of incorrectly posed problems and a method of regularization,” Dokl. Akad. Nauk SSSR,151, No. 3, 501–504 (1963).

    Google Scholar 

  3. A. N. Tikhonov, “On regularization of incorrectly posed problems,” Dokl. Akad. Nauk SSSR,153, No. 1, 49–52 (1963).

    Google Scholar 

  4. V. K. Ivanov, “On the approximate solution of operator equations of first kind,” Zh. Vychisl. Mat. Mat. Fiz.,6, No. 6, 1089–1095 (1966).

    Google Scholar 

  5. V. P. Tanana and V. A. Korshunov, “The principle of minimal remainders,” Dokl. Akad. Nauk SSSR,239, No. 4, 800–803 (1978).

    Google Scholar 

  6. V. K. Ivanov, “On linear incorrect problems,” Dokl. Akad. Nauk SSSR,145, No. 2, 270–272 (1962).

    Google Scholar 

  7. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Incorrect Problems, [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  8. J. C. Phillips, “Critical points and lattice vibration spectra,” Phys. Rev.,104, No. 5, 1263–1277 (1956).

    Google Scholar 

  9. B. I. Gorbachev, P. G. Ivanitskii, V. T. Krotenko, and M. V. Pasechnik, “Investigation of inelastic scattering of slow neutrons on specimens of nickel with various isotopic compositions,” Ukr. Fiz. Zh.,18, No. 4, 558–563 (1973).

    Google Scholar 

  10. R. J. Birgeneau, J. Cordes, G. Dolling, and A. D. B. Woods, “Normal modes of vibration in nickel,” Phys. Rev.,136, No. SA, 1359–1365 (1964).

    Google Scholar 

  11. I. P. Eremeev, I. P. Sadikov, and A. A. Chernyshov, “The density of phonon states in hexagonal metals of group II,” Fiz. Tverd. Tela,18, No. 6, 1652–1660 (1976).

    Google Scholar 

  12. N. J. Chesser and J. D. Axe, “Lattice dynamics of zinc: phonon structure factors,” Phys. Rev. B,9, No. 10, 4060–4067 (1974).

    Google Scholar 

  13. B. A. Nesterenko, B. I. Gorbachev, V. A. Zrazhevskii, P. G. Ivanitskii, V. T. Krotenko M. V. Pasechnik, and O. V. Snitko, “The phonon spectrum of the silicon lattice,” Fiz. Tverd. Tela,16, No. 11, 3513–3515 (1974).

    Google Scholar 

  14. R. Tubino, L. Piseri, and G. Zerbi, “Lattice dynamics and spectroscopic properties by a valence force potential of dia mondlike crystals: C, Si, Ge, and Sn,” J. Chem. Phys.,56, No. 3, 1022–1039 (1972).

    Google Scholar 

  15. G. Dolling, “Lattice vibrations in crystals with the diamond structure,” in: Inelastic Scattering of Neutrons in Solids and Liquids, Vol. 2, IAEA, Vienna (1963), pp. 37–47.

    Google Scholar 

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A. M. Gorki Ural State University, Sverdlovsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 4, pp. 161–168, July–August, 1980.

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Tanana, V.P., Korshunov, V.A. Choice of regularization parameter in solving incorrect problems. Sib Math J 21, 602–607 (1980). https://doi.org/10.1007/BF00995963

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