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Zh. Vychisl. Mat. Mat. Fiz., 1980, Volume 20, Number 6, Pages 1373–1383 (Mi zvmmf5156)  

This article is cited in 17 scientific papers (total in 18 papers)

Approximate systems of linear algebraic equations

A. N. Tikhonov

Moscow

Full text: PDF file (1052 kB)

English version:
USSR Computational Mathematics and Mathematical Physics, 1980, 20:6, 10–22

Bibliographic databases:

UDC: 519.612
MSC: Primary 65F05; Secondary 65F20, 65G50
Received: 11.08.1980

Citation: A. N. Tikhonov, “Approximate systems of linear algebraic equations”, Zh. Vychisl. Mat. Mat. Fiz., 20:6 (1980), 1373–1383; U.S.S.R. Comput. Math. Math. Phys., 20:6 (1980), 10–22

Citation in format AMSBIB
\Bibitem{Tik80}
\by A.~N.~Tikhonov
\paper Approximate systems of linear algebraic equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1980
\vol 20
\issue 6
\pages 1373--1383
\mathnet{http://mi.mathnet.ru/zvmmf5156}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=609319}
\zmath{https://zbmath.org/?q=an:0492.65014}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1980
\vol 20
\issue 6
\pages 10--22
\crossref{https://doi.org/10.1016/0041-5553(80)90003-8}


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    This publication is cited in the following articles:
    1. A. V. Bitsadze, V. A. Il'in, O. A. Oleinik, Yu. P. Popov, A. A. Samarskii, A. G. Sveshnikov, S. L. Sobolev, “Andrei Nikolaevich Tikhonov (on his eightieth birthday)”, Russian Math. Surveys, 42:3 (1987), 1–12  mathnet  crossref  mathscinet  adsnasa  isi
    2. A. S. Leonov, “The minimum pseudo-inverse matrix method: Theory and numerical implementation”, U.S.S.R. Comput. Math. Math. Phys., 31:10 (1991), 1–13  mathnet  mathscinet  zmath  isi
    3. A. S. Mechenov, “Partially approximate systems of linear algebraic equations”, U.S.S.R. Comput. Math. Math. Phys., 31:6 (1991), 6–12  mathnet  mathscinet  zmath  isi
    4. V. Ya. Arsenin, A. V. Kryanev, “A generalized maximum-likelihood method for solving finite-dimensional ill-posed problems”, U.S.S.R. Comput. Math. Math. Phys., 31:5 (1991), 1–8  mathnet  mathscinet  zmath  isi
    5. V. K. Gorbunov, “Regularization of extremal problems”, U.S.S.R. Comput. Math. Math. Phys., 31:2 (1991), 42–52  mathnet  mathscinet  zmath  isi
    6. S. F. Gilyazov, “Regularizing conjugate-direction methods”, Comput. Math. Math. Phys., 35:4 (1995), 385–394  mathnet  mathscinet  zmath  isi
    7. A. I. Zhdanov, “Regularization of unstable finite-dimensional linear problems based on augmented systems”, Comput. Math. Math. Phys., 45:11 (2005), 1845–1855  mathnet  mathscinet  zmath
    8. V. I. Erokhin, “Matrix correction of a dual pair of improper linear programming problems”, Comput. Math. Math. Phys., 47:4 (2007), 564–578  mathnet  crossref  mathscinet  zmath
    9. V. I. Erokhin, V. V. Volkov, “Postroenie modelnykh priblizhennykh sistem lineinykh algebraicheskikh uravnenii s izvestnymi tikhonovskimi resheniyami”, Sib. elektron. matem. izv., 7 (2010), 207–217  mathnet
    10. V. V. Volkov, V. I. Erokhin, “Tikhonov solutions of approximate systems of linear algebraic equations under finite perturbations of their matrices”, Comput. Math. Math. Phys., 50:4 (2010), 589–605  mathnet  crossref  mathscinet  adsnasa  isi
    11. Erokhin V.I., Volkov V.V., “Priblizhennye lineinye modeli v zadachakh pozitsionirovaniya s ispolzovaniem globalnykh sputnikovykh navigatsionnykh sistem”, Sistemy upravleniya i informatsionnye tekhnologii, 42:4.1 (2010), 145–149  elib
    12. O. V. Murav'eva, “Robustness and correction of linear models”, Autom. Remote Control, 72:3 (2011), 556–569  mathnet  crossref  mathscinet  zmath  isi
    13. Erokhin V.I., Volkov V.V., “Metody i modeli vosstanovleniya lineinykh zavisimostei po netochnoi informatsii”, Izvestiya Sankt-Peterburgskogo gosudarstvennogo tekhnologicheskogo instituta (tekhnicheskogo universiteta), 2011, no. 10, 52–57  elib
    14. V. I. Erokhin, A. S. Krasnikov, M. N. Khvostov, “Matrix corrections minimal with respect to the Euclidean norm for linear programming problems”, Autom. Remote Control, 73:2 (2012), 219–231  mathnet  crossref  isi
    15. V. I. Erokhin, “O nekotorykh dostatochnykh usloviyakh razreshimosti i nerazreshimosti zadach matrichnoi korrektsii nesobstvennykh zadach lineinogo programmirovaniya”, Tr. IMM UrO RAN, 21, no. 3, 2015, 110–116  mathnet  mathscinet  elib
    16. V. I. Erokhin, V. V. Volkov, “O regulyarizovannom metode naimenshikh kvadratov A. N. Tikhonova”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 13:1 (2017), 4–16  mathnet  crossref  elib
    17. V. V. Volkov, V. I. Erokhin, V. V. Kakaev, A. Yu. Onufrei, “Generalizations of Tikhonov's regularized method of least squares to non-Euclidean vector norms”, Comput. Math. Math. Phys., 57:9 (2017), 1416–1426  mathnet  crossref  crossref  isi  elib  elib
    18. V. V. Volkov, V. I. Erokhin, A. S. Krasnikov, A. V. Razumov, M. N. Khvostov, “Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems”, Comput. Math. Math. Phys., 57:11 (2017), 1757–1770  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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