Nikolai Sergeevich Bakhvalov (russian: Николай Серге́евич Бахвалов) (May 29, 1934 – August 29, 2005) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

and

Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. Born in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

into the family of Sergei Vladimirovich Bakhvalov, a geometer at

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

, N.S. Bakhvalov was exposed to mathematics from a young age. In 1950, Bakhvalov entered the Faculty of Mechanics and Mathematics at Moscow State University. His supervisors there included

Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

and Sobolev. Bakhvalov defended his doctorate in 1958. He was a professor of mathematics at Moscow State University since 1966, specializing in

computational mathematics Computational mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation.National Science Foundation, Division of Mathematical ScienceProgram description PD 06-888 Computational Mathematics 2006 ...

. Bakhvalov was a member of the Russian Academy of Sciences since 1991 and a head of the department of computational mathematics at the college of mechanics and mathematics of the Moscow State University since 1981. Bakhvalov authored over 150 papers, several books, and a popular textbook on numerical methods. He had made major pioneering contributions to many areas of mathematics and mechanics. Starting early in his career, Bakhvalov formulated and proved important results on the optimization of

numerical algorithms Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distin ...

. In 1959, he determined the

complexity Complexity characterises the behaviour of a system or model whose components interaction, interact in multiple ways and follow local rules, leading to nonlinearity, randomness, collective dynamics, hierarchy, and emergence. The term is generall ...

of the integration problem in the worst-case setting for integrands of smoothness. Furthermore, he proposed an optimal algorithm for the randomized setting. These can be considered early results in the theory of

information-based complexity Information-based complexity (IBC) studies optimal algorithms and computational complexity for the continuous problems that arise in physical science, economics, engineering, and mathematical finance. IBC has studied such continuous problems as pat ...

. Bakhvalov was one of the pioneers of the

multigrid method In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhi ...

, contributed to the theory of

homogenization Homogeneity is a sameness of constituent structure. Homogeneity, homogeneous, or homogenization may also refer to: In mathematics *Transcendental law of homogeneity of Leibniz * Homogeneous space for a Lie group G, or more general transformati ...

, and fictitious domain methods. Bakhvalov supervised 47 Ph.D. students and was an advisor to 11

doctorates A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''li ...

Notes

* http://www.netlib.org/na-digest-html/06/v06n04.html#5 Nikolaj S. Bakhvalov: May 29, 1934 - August 29, 2005
From RAS

Bakhvalov is sixty

References

* *N. S. Bakhvalov (1966) On the convergence of a relaxation method with natural constraints on the elliptic operator. USSR Comp. Math. Math. Phis.6, 101–13. *''Homogenisation: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Materials'' (1989), N. S. Bakhvalov, G. Panasenko, Springer, *N. S. Bakhvalov and A. V. Knyazev (1994
Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components
In Numerical Methods and Applications, Ed. Gury I. Marchuk, CRC Press, 221-276. *

External links

Nikolai Bakhvalov — scientific works on the website Math-Net.Ru
* * {{DEFAULTSORT:Bakhvalov, Nikolai Russian mathematicians Soviet mathematicians Numerical analysts Moscow State University alumni Academic staff of Moscow State University Corresponding Members of the USSR Academy of Sciences Full Members of the Russian Academy of Sciences 1934 births 2005 deaths