Andrey Tikhonov (mathematician)
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Andrey Nikolayevich Tikhonov
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ill-posed problems ;
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| Fields | Alexei Georgievich Sveshnikov |
Andrey Nikolayevich Tikhonov (
ill-posed problems. He was also one of the inventors of the magnetotellurics
method in geophysics. Other transliterations of his surname include "Tychonoff", "Tychonov", "Tihonov", "Tichonov".
Biography
Born in
USSR Academy of Sciences on 29 January 1939 and a full member
of the USSR Academy of Sciences on 1 July 1966.
Research work
Tikhonov worked in a number of different fields in mathematics. He made important contributions to
completely regular topological spaces are also named Tychonoff spaces
.
In mathematical physics, he proved the fundamental uniqueness theorems for the heat equation[2] and studied Volterra integral equations.
He founded the theory of asymptotic analysis for differential equations with small parameter in the leading derivative.[3]
Organizer work
Tikhonov played the leading role in founding the Faculty of Computational Mathematics and Cybernetics of Moscow State University and served as its first dean during the period of 1970–1990.
Awards
Tikhonov received numerous honors and awards for his work, including the
Hero of Socialist Labor
(1954, 1986).
Publications
Books
- Sveshnikov, A. G.; Tikhonov, A. N. (1978). The Theory of Functions of a Complex Variable. Mir. (English translation.)
- Tikhonov, A. N.; Arsenin, V. Y. (1977). Solutions of Ill-Posed Problems. New York: Winston. ISBN 0-470-99124-0.[4]
- Tikhonov, A. N.; Goncharsky, A. V. (1987). Ill-posed Problems in the Natural Sciences. Oxford: Oxford University Press. ISBN 0-8285-3739-9.
- A. N., Tikhonov; ISBN 978-0-48-617336-8.
- Tikhonov, A. N.; Goncharsky, A. V.; Stepanov, V. V.; Yagola, A. G. (1995). Numerical Methods for the Solution of Ill-Posed Problems. Dordrecht: Kluwer. ISBN 0-7923-3583-X.
- Tikhonov, A. N.; Leonov, A. S.; Yagola, A. G. (1998). Nonlinear Ill-Posed Problems. Vol. 1–2. London, Weinheim, New York, Tokyo, Melbourne, Madras: Chapman and Hall. ISBN 0-412-78660-5.
Papers
- Tikhonov, A. N.; Samarskii, A. A. (1962). "Homogeneous difference schemes". USSR Computational Mathematics and Mathematical Physics. 1: 5–67. .
- Tikhonov, A. N.; Samarskii, A. A. (1963). "Homogeneous difference schemes on non-uniform nets" (PDF). USSR Computational Mathematics and Mathematical Physics. 2 (5): 927–953. .
- Tikhonov, A. N. (1966). "On the stability of the functional optimization problem". USSR Computational Mathematics and Mathematical Physics. 6 (4): 28–33. .
See also
- Regularization
- Stone–Čech compactification
- Tikhonov cube
- Tikhonov distribution
- Tikhonov plank
- Tikhonov space
- Tikhonov's theorem on dynamical systems
References
- ^ Andrei Nikolaevich Tikhonov at the Mathematics Genealogy Project
- ^ A. Tychonoff (1935). "Théorèmes d'unicité pour l'équation de la chaleur". Matematicheskii Sbornik. 42 (2): 199–216.
- ^ A. N. Tikhonov (1952). "Systems of Differential Equations Containing Small Parameters in the Derivatives". Mathematical Sbornik. 31 (73): 3.
- ISSN 0273-0979.
External links
- O'Connor, John J.; Robertson, Edmund F., "Andrey Tikhonov (mathematician)", MacTutor History of Mathematics Archive, University of St Andrews
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