Nikolai Sergeevich Bakhvalov () (May 29, 1934 – August 29, 2005) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

and

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

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, mathematical structure, structure, space, Mathematica ...

. Born in

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

into the family of Sergei Vladimirovich Bakhvalov, a geometer at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

, 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 Soviet ...

and

Sobolev Sobolev (masculine) and Soboleva (feminine) is a popular Russian surname, derived from the word ''"соболь"'' (sable The sable (''Martes zibellina'') is a species of marten, a small omnivorous mammal primarily inhabiting the forest enviro ...

. 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 the study of the interaction between mathematics and calculations done by a computer.National Science Foundation, Division of Mathematical ScienceProgram description PD 06-888 Computational Mathematics 2006. Retri ...

. 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. In 1959, he determined the

complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...

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 Mathematical finance, also known as quantitativ ...

. 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 e ...

, contributed to the theory of homogenization, and fictitious domain methods. Bakhvalov supervised 47 Ph.D. students and was an advisor to 11

doctorates A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

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