Andrew Knyazev is an American mathematician. He graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University under the supervision of Evgenii Georgievich D'yakonov (Russian: Евгений Георгиевич Дьяконов) in 1981 and obtained his PhD in Numerical Mathematics at the Russian Academy of Sciences under the supervision of Vyacheslav Ivanovich Lebedev (Russian: Вячеслав Иванович Лебедев) in 1985. He worked at the Kurchatov Institute between 1981–1983, and then to 1992 at the Marchuk Institute of Numerical Mathematics (Russian: ru:Институт вычислительной математики имени Г. И. Марчука РАН) of the Russian Academy of Sciences, headed by Gury Marchuk (Russian: Гурий Иванович Марчук).
Andrew Knyazev | |
|---|---|
 Andrew Knyazev | |
| Born | |
| Alma mater | Moscow State University |
| Known for | eigenvalue solvers |
| Awards | IEEE Senior Member (2013) Professor Emeritus University of Colorado Denver (2016) SIAM Fellow (2016) AMS Fellow (2019) |
| Scientific career | |
| Fields | Numerical analysis, Applied Mathematics, Computer Science |
| Institutions | Kurchatov Institute Institute of Numerical Mathematics Russian Academy of Sciences Courant Institute of Mathematical Sciences New York University University of Colorado Denver Mitsubishi Electric Research Laboratories |
| Doctoral advisor | Vyacheslav Ivanovich Lebedev |
| Website | https://www.linkedin.com/in/andrew-knyazev/ |
From 1993–1994, Knyazev held a visiting position at the Courant Institute of Mathematical Sciences of New York University, collaborating with Olof B. Widlund.[1] From 1994 until retirement in 2014, he was a Professor of Mathematics at the University of Colorado Denver, supported by the National Science Foundation[2] and United States Department of Energy grants. He was a recipient of the 2008 Excellence in Research Award,[3] 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.[4] He was awarded the title of Professor Emeritus at the University of Colorado Denver[5] and named the SIAM Fellow Class of 2016[6] and AMS Fellow Class of 2019.[7]
From 2012–2018, Knyazev worked at the Mitsubishi Electric Research Laboratories[8] on algorithms for image and video processing, data sciences, optimal control, and material sciences, resulting in dozens of publications and 13 patent applications.[9] Since 2018, he contributed to numerical techniques in quantum computing at Zapata Computing, real-time embedded anomaly detection in automotive data, and algorithms for silicon photonics-based hardware.
Knyazev is mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly preconditioning[10] and the iterative method LOBPCG.[11] Knyazev's implementation of LOBPCG is available in many open source software packages, e.g., BLOPEX, SciPy, and ABINIT.[12]
Knyazev collaborated with John Osborn [13] on the theory of the Ritz method in the finite element method context and with Nikolai Sergeevich Bakhvalov (Russian: Николай Серге́евич Бахвалов) (Erdős number 3 via Leonid Kantorovich) on numerical solution of elliptic partial differential equations with large jumps in the main coefficients.[14] Jointly with his Ph.D. students, Knyazev pioneered using majorization for bounds in the Rayleigh–Ritz method (see[15] and references there) and contributed to the theory of angles between flats.[16] [17]
References
edit- ^ Knyazev, Andrew; Widlund, Olof (2003), "Lavrentiev Regularization + Ritz Approximation = Uniform Finite Element Error Estimates for Differential Equations with Rough Coefficients", Mathematics of Computation, 72 (241): 17–40, doi:10.1090/S0025-5718-01-01378-3
- ^ Knyazev's NSF awards
- ^ Andrew Knyazev. 2008 Excellence in Research and Creative Activities Award Winner, 1 May 2008, archived from the original on 8 September 2011, retrieved 12 January 2016
- ^ Goodland, Marianne (6 May 1999), "President's Faculty Excellence Award for Advancing Teaching and Learning through Technology", Silver & Gold Record, XXIX (34)
- ^ Professor Emeritus University of Colorado Denver, 6 January 2016
- ^ Society for Industrial and Applied Mathematics (SIAM) Fellows Class of 2016, 31 March 2016
- ^ American Mathematical Society (AMS) Fellows Class of 2019, 31 October 2018
- ^ Andrew Knyazev moved to MERL, 2012
- ^ Knyazev's Website at Mitsubishi Electric Research Laboratories Archived January 20, 2018, at the Wayback Machine
- ^ Knyazev, A.V. (1998), "Preconditioned eigensolvers - an oxymoron?" (PDF), Electron. Trans. Numer. Anal., 7: 104–123
- ^ Knyazev, A.V. (2001), "Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method", SIAM Journal on Scientific Computing, 23 (2): 517–541, Bibcode:2001SJSC...23..517K, doi:10.1137/S1064827500366124
- ^ Bottin, F.; Leroux, S.; Knyazev, A.; Zerah, G. (2008), "Large scale ab initio calculations based on three levels of parallelization", Computational Materials Science, 42 (2): 329–336, arXiv:0707.3405, doi:10.1016/j.commatsci.2007.07.019, S2CID 6206246
- ^ Knyazev, A.V.; Osborn, J. (2006), "New A Priori FEM Error Estimates for Eigenvalues", SIAM J. Numer. Anal., 43 (6): 2647–2667, doi:10.1137/040613044
- ^ Bakhvalov, N.S.; Knyazev, A.V.; Parashkevov, R.R. (2002), "Extension Theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients", Numerical Linear Algebra with Applications, 9 (2): 115–139, doi:10.1002/nla.259, S2CID 14266720
- ^ Knyazev, A.V.; Argentati, M.E. (2010), "Rayleigh–Ritz majorization error bounds with applications to FEM", SIAM J. Matrix Anal. Appl., 31 (3): 1521–1537, arXiv:math/0701784, doi:10.1137/08072574X, S2CID 1390330
- ^ Knyazev, A.V.; Argentati, M.E. (2006), "Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra", SIAM J. Matrix Anal. Appl., 29 (1): 15–32, arXiv:math/0508591, doi:10.1137/060649070, S2CID 16987402
- ^ Knyazev, A.V.; Jujunashvili, A.; Argentati, M.E. (2010), "Angles between infinite dimensional subspaces with applications to the Rayleigh–Ritz and alternating projectors methods", Journal of Functional Analysis, 259 (6): 1323–1345, arXiv:0705.1023, doi:10.1016/j.jfa.2010.05.018, S2CID 5570062
External links
edit- Andrei Knyazev publications indexed by Google Scholar
- Andrei Knyazev's publications indexed by the Scopus bibliographic database. (subscription required)
- Andrei Knyazev at the Mathematics Genealogy Project
- Patents granted to Andrei Kniazev and patent applications filed by Andrei Kniazev at USPTO and world-wide
- MathSciNet (subscription required) reviews for Andrew Knyazev
- Zentralblatt MATH reviews
- ORCID [1]
- arXiv Reports
- SIGPORT Contributions
- Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) at GitHub
- Knyazev's software in MATLAB
- Andrei Knyazev on LinkedIn
- Andrew Knyazev on ResearchGate