Andrew Knyazev is an American

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 ...

. He graduated from the Faculty of Computational Mathematics and Cybernetics of

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 ...

under the supervision of

Evgenii Georgievich D'yakonov Evgenii Georgievich Dyakonov () (July 2, 1935 – August 11, 2006) was a Russian mathematician. Dyakonov was a Ph.D. student of Sergei Sobolev. He worked at the Moscow State University. He authored over hundred papers and several books. Dy ...

() in 1981 and obtained his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

Numerical Mathematics Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

at the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

under the supervision of

Vyacheslav Ivanovich Lebedev Vyacheslav Ivanovich Lebedev () (January 27, 1930 – March 22, 2010) was a USSR, Soviet and Russian mathematician, known for his work on numerical analysis. Career Lebedev was a Ph.D. student of Sergei Sobolev, Sobolev. He worked at the Kurch ...

() in 1985. He worked at the

Kurchatov Institute The Kurchatov Institute (, National Research Centre "Kurchatov Institute") is Russia's leading research and development institution in the field of nuclear power, nuclear energy. It is named after Igor Kurchatov and is located at 1 Kurchatov Sq ...

between 1981–1983, and then to 1992 at th
Marchuk Institute of Numerical Mathematics
() of the

, headed by

Gury Marchuk Gury Ivanovich Marchuk (; 8 June 1925 – 24 March 2013) was a Soviet and Russian scientist in the fields of computational mathematics, and physics of atmosphere. Academician (since 1968); the President of the USSR Academy of Sciences in 198 ...

(). From 1993–1994, Knyazev held a visiting position at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

, collaborating with

Olof B. Widlund Olof B. Widlund (born 1938), is a Swedish-American mathematician. He is well known for his leading role in and fundamental contributions to domain decomposition methods. He received his Ph.D. at Uppsala University in 1966 and is professor of comp ...

. From 1994 until retirement in 2014, he was a Professor of

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at the

University of Colorado Denver The University of Colorado Denver (CU Denver) is a Public university, public research university located in downtown Denver, Colorado. It is part of the University of Colorado system. Established in 1912 as an extension of the University of C ...

, supported by the

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

and

United States Department of Energy The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and energy production, the research and development of nuclear power, the military's nuclear w ...

grants. He was a recipient of the 2008 Excellence in Research Award, the 2000 college Teaching Excellence Award, and a finalist of the CU President's Faculty Excellence Award for Advancing Teaching and Learning through Technology in 1999. He was awarded the title of Professor Emeritus at the

and named the

SIAM Thailand, officially the Kingdom of Thailand and historically known as Siam (the official name until 1939), is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. With a population of almost 66 million, it spa ...

Fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

Class of 2016 and

AMS AMS or Ams may refer to: Organizations Companies * Alenia Marconi Systems * American Management Systems * AMS (Advanced Music Systems) * ams AG, semiconductor manufacturer * AMS Pictures * Auxiliary Medical Services Educational institutions ...

Class of 2019. From 2012–2018, Knyazev worked at the

Mitsubishi Electric Research Laboratories Mitsubishi Electric Research Laboratories (MERL) is a subsidiary of Mitsubishi Electric US Holdings, Inc., which is the principal subsidiary of Mitsubishi Electric in the United States. MERL acts as North American arm of Mitsubishi's Corporate R& ...

on algorithms for image and video processing, data sciences, optimal control, and material sciences, resulting in dozens of publications and 13 patent applications. Since 2018, he contributed to numerical techniques in

quantum computing A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of wave-particle duality, both particles and waves, and quantum computing takes advantage of this behavior using s ...

a
Zapata Computing
real-time embedded

anomaly detection In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of ...

in automotive data, and algorithms for

silicon photonics Silicon photonics is the study and application of photonic systems which use silicon as an optical medium. The silicon is usually patterned with sub-micrometre precision, into microphotonic components. These operate in the infrared, most commo ...

-based hardware. Knyazev is mostly known for his work in numerical solution of large

sparse Sparse is a computer software tool designed to find possible coding faults in the Linux kernel. Unlike other such tools, this static analysis tool was initially designed to only flag constructs that were likely to be of interest to kernel deve ...

eigenvalue problem In linear algebra, an eigenvector ( ) or characteristic vector is a Vector (mathematics and physics), vector that has its direction (geometry), direction unchanged (or reversed) by a given linear map, linear transformation. More precisely, an e ...

s, particularly

preconditioning In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing ...

and the iterative method

LOBPCG Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem :A x= \lambda B x, for a g ...

. Knyazev's implementation of

is available in many open source software packages, e.g.,

BLOPEX Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free methods, matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem :A x= \ ...

SciPy SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, fast Fourier ...

, and

ABINIT ABINIT is an open-source suite of programs for materials science, distributed under the GNU General Public License. ABINIT implements density functional theory, using a plane wave basis set and pseudopotentials, to compute the electronic density a ...

. Knyazev collaborated with John Osborn on the theory of the

Ritz method Ritz or The Ritz may refer to: Facilities and structures Hotels * The Ritz Hotel, London, a hotel in London, England ** Ritz Club casino * Hôtel Ritz Paris, a hotel in Paris, France * Hotel Ritz (Madrid), a hotel in Madrid, Spain * Hotel Ritz ...

in the

finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...

context and with

Nikolai Sergeevich Bakhvalov Nikolai Sergeevich Bakhvalov () (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 ...

() (

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

3 via

Leonid Kantorovich Leonid Vitalyevich Kantorovich (, ; 19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programm ...

) on numerical solution of

elliptic partial differential equations In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently used to model steady states, unlike parabolic PDE and hyperbolic PDE which gener ...

with large jumps in the main coefficients. Jointly with his Ph.D. students, Knyazev pioneered using

majorization In mathematics, majorization is a preorder on vector space, vectors of real numbers. For two such vectors, \mathbf,\ \mathbf \in \mathbb^n, we say that \mathbf weakly majorizes (or dominates) \mathbf from below, commonly denoted \mathbf \suc ...

for bounds in the

Rayleigh–Ritz method The Rayleigh–Ritz method is a direct numerical method of approximating eigenvalues, originated in the context of solving physical boundary value problems and named after Lord Rayleigh and Walther Ritz. In this method, an infinite-dimensiona ...

(see and references there) and contributed to the theory of

angles between flats The concept of angles between lines (in the plane or in space), between two planes ('' dihedral angle'') or between a line and a plane can be generalized to arbitrary dimensions. This generalization was first discussed by Camille Jordan. For any ...

References

External links

* * *
Patents granted to Andrei Kniazev
an

at

USPTO The United States Patent and Trademark Office (USPTO) is an agency in the U.S. Department of Commerce that serves as the national patent office and trademark registration authority for the United States. The USPTO's headquarters are in Ale ...

and ttp://www.freepatentsonline.com/result.html?sort=relevance&srch=top&query_txt=Andrei+Kniazev&submit=&patents=on# world-wide*

MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...

(subscription required
reviews for Andrew Knyazev
*

Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

br>reviews
*

ORCID The ORCID (; Open Researcher and Contributor ID) is a nonproprietary alphanumeric code to uniquely identify authors and contributors of scholarly communication. This addresses the problem that a particular author's contributions to the scien ...

br>
*

arXiv arXiv (pronounced as "archive"—the X represents the Chi (letter), Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not Scholarly pee ...

br>Reports
*SIGPOR
ContributionsBlock Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX)
at

GitHub GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug trackin ...

Knyazev's software
in

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

*
Andrew Knyazev
on

ResearchGate ResearchGate is a European commercial social networking site for scientists and researchers to share papers, ask and answer questions, and find collaborators. According to a 2014 study by ''Nature'' and a 2016 article in ''Times Higher Education' ...

{{DEFAULTSORT:Knyazev, Andrei 20th-century American mathematicians 21st-century American mathematicians Soviet mathematicians Moscow State University alumni 1959 births Living people University of Colorado Denver faculty American applied mathematicians Numerical analysts Machine learning researchers Senior members of the IEEE Fellows of the Society for Industrial and Applied Mathematics Mitsubishi Electric people Fellows of the American Mathematical Society