mathematics

Nikolai Bakhvalov

Nikolai Bakhvalov is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nikolai Bakhvalov rather than just read about it. In short: Nikolai Sergeevich Bakhvalov (Russian: Николай Серге́евич Бахвалов) (May 29, 1934 – August 29, 2005) was a Soviet and Russian mathematician. Born in Moscow into the family of Sergei Vladimirovich Bakhvalov, a geometer at Moscow State University, N.S.

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Reference excerpt

Nikolai Sergeevich Bakhvalov (Russian: Николай Серге́евич Бахвалов) (May 29, 1934 – August 29, 2005) was a Soviet and Russian mathematician. Born in Moscow into the family of Sergei Vladimirovich Bakhvalov, a geometer at Moscow State University, 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 and Sobolev. Bakhvalov defended his doctorate in 1958. He was a professor of mathematics at Moscow State University since 1966, specializing in computational mathematics. 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 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. Bakhvalov was one of the pioneers of the multigrid method, contributed to the theory of homogenization, and fictitious domain methods. Bakhvalov supervised 47 Ph.D. students and was an advisor to 11 doctorates.

Notes https://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 Bakhvalov, N.S. (1959), "On the approximate calculation of integrals.", Vestnik MGU, Ser. Mat. Mekh. Astron. Fiz. Khim., 4: 2–18 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, ISBN 978-0-7923-0049-6 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. ISBN 978-0-8493-8947-4 Kerimov, M. K. (2006), "Academician Nikolai Sergeevich Bakhvalov (1934--2005)", Computational Mathematics and Mathematical Physics, 46 (1): 182–184, Bibcode:2006CMMPh..46..182K, doi:10.1134/S0965542506010179, S2CID 121126321

External links Nikolai Bakhvalov — scientific works on the website Math-Net.Ru Nikolai Bakhvalov at zbMATH Nikolai Bakhvalov at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Nikolai Bakhvalov

Start with the simplest possible case. Write down what Nikolai Bakhvalov claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nikolai Bakhvalov before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nikolai Bakhvalov ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nikolai Bakhvalov

In research: Nikolai Bakhvalov appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nikolai Bakhvalov in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nikolai Bakhvalov is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1934 births, 2005 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Nikolai Bakhvalov outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

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Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

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Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

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