Andrei Nikolaevich Tikhonov

Tikhonov, Andrei Nikolaevich

 

Born Oct. 17 (30), 1906, in Gzhatsk, now the city of Gagarin, Smolensk Oblast. Soviet mathematician and geophysicist. Academician of the Academy of Sciences of the USSR (1966; corresponding member, 1939). Hero of Socialist Labor (1953).

Tikhonov graduated from Moscow State University in 1927. He became a professor at the university in 1936 and was made head of the department of computing mathematics and cybernetics in 1970. In 1953 he was appointed deputy director of the Institute of Applied Mathematics of the Academy of Sciences of the USSR.

Tikhonov’s first works were devoted to topology and functional analysis. In 1926 he introduced the concept of the product space of topological spaces. He proved that the product of compact spaces is compact and that there exists a fixed point in continuous mappings in topological spaces.

In his subsequent works, Tikhonov made contributions to the theory of differential equations, mathematical physics, geophysics, and computational mathematics. He proved uniqueness theorems for the heat equation in 1935 and 1937 and studied functional equations of the Volterra type in 1938. With a paper published in 1948, he became one of the founders of the theory of differential equations with a small parameter in the highest-order derivative. Tikhonov carried out fundamental research, published in 1950, on the theory and methods of the application of electromagnetic fields to the study of the internal structure of the earth’s crust. Under his direction algorithms were created for the solution of many applied problems. Between 1956 and 1963, Tikhonov, together with A. A. Samarskii, developed the theory of uniform difference schemes. In works published in 1943 and 1963, he introduced a regularization concept that permitted the development of methods for solving incorrect problems, in particular, many inverse problems of classical mathematics and the natural sciences.

Tikhonov received the State Prize of the USSR in 1953 and 1976 and the Lenin Prize in 1966. He has been awarded five Orders of Lenin, four other orders, and several medals.

WORKS

Uravneniia matematicheskoi fiziki, 4th ed. Moscow, 1972. (With A. A. Samarskii.)
Teoriia funktsii kompleksnoi peremennoi, 3rd ed. Moscow, 1974. (With A. G. Sveshnikov.)
Metody resheniia nekorrektnykh zadach. Moscow, 1974. (With V. Ia. Arsenin.)

REFERENCE

“Andrei Nikolaevich Tikhonov.” Uspekhi matematicheskikh nauk, 1956, vol. 11, issue 6; 1967, vol. 22, issue 2. (Contains bibliography.)

A. G. SVESHNIKOV

References in periodicals archive ?
Basing their work on that of the Russian mathematical pioneer Andrei Nikolaevich Tikhonov, the authors explain Russian techniques in inverse mathematical problems, boundary value problems for ordinary differential equations, boundary value problems for elliptic equations, boundary value problems for parabolic equations, solution methods for ill-posed problems (to which inverse mathematical physics problems often belong), right-hand side identification, evolutionary inverse problems and other problems, including non-local distribution of boundary conditions.

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