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Problem of precision of the method of a minimal pseudoinverse matrix

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Literature cited

  1. R. D. Penrose, “A generalized inverse for matrices,” Proc. Cambr. Philos. Soc.,51, 406–413 (1955).

    Google Scholar 

  2. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. A. N. Tikhonov, “On problems with an imprecisely given information,” Dokl. Akad. Nauk USSR,280, No. 3, 559–562 (1985).

    Google Scholar 

  4. V. A. Morozov, “On pseudosolutions,” Zh. Vychisl. Mat. Mat. Fiz.,9, No. 6, 1387–1391 (1969).

    Google Scholar 

  5. V. V. Voevodin, Computational Foundations of Linear Algebra [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  6. Ch. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Prentice Hall, N. J. (1974).

    Google Scholar 

  7. S. F. Gilyazov and V. A. Morozov, “Optimal regularization of normally solvable operator equations,” Zh. Vychisl. Mat. Mat. Fiz.,24, No. 1, 1737–1742 (1984).

    Google Scholar 

  8. I. V. Kochikov, A. N. Matvienko, and A. G. Yagola, “A generalized principle of residuals for solving incompatible equations,” Zh. Vychisl. Mat. Mat. Fiz.,24, No. 7, 1087–1090 (1984).

    Google Scholar 

  9. G. M. Vainikko and A. Yu. Veretennikov, Iteration Procedures in Ill-Posed Problems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  10. G. M. Golub, “Least squares, singular values and matrix approximation,” Aplik. Mat.,13, No. 1, 44–51 (1968).

    Google Scholar 

  11. A. S. Leonov, “The method of minimal pseudoinverse matrix and solution of ill-posed problems of linear algebra based on it,” in: Theory and Methods of Solving Ill-Posed Problems and Their Applications, Novosibirsk University Press (1983), pp. 49–52.

  12. A. S. Leonov, “The method of minimal pseudoinverse matrix,” Zh. Vychisl. Mat. Mat. Fiz.,27, No. 8, 1123–1138 (1987).

    Google Scholar 

  13. P. A. Wedin, “Perturbation theory for pseudo-inverses,” BIT,13, 217–232 (1973).

    Google Scholar 

  14. Ya. Busha, “On a method of regularization of a solution of a system of linear algebraic equations,” Dokl. Akad. Nauk USSR,295, No. 1, 11–14 (1987).

    Google Scholar 

  15. V. P. Tanana, Methods for Solving Operator Equations [in Russian], Nauka, Moscow (1981).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 49, No. 4, pp. 81–87, April, 1991.

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Leonov, A.S. Problem of precision of the method of a minimal pseudoinverse matrix. Mathematical Notes of the Academy of Sciences of the USSR 49, 386–390 (1991). https://doi.org/10.1007/BF01158215

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