Andrew Knyazev
Andrew Knyazev
Born
Moscow, Soviet Union
Alma materMoscow State University
Known foreigenvalue solvers
AwardsIEEE Senior Member (2013)
Professor Emeritus University of Colorado Denver (2016)
SIAM Fellow (2016)
AMS Fellow (2019)
Scientific career
FieldsNumerical analysis, Applied Mathematics, Computer Science
InstitutionsKurchatov 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 advisorVyacheslav Ivanovich Lebedev
Websitehttps://www.linkedin.com/in/andrew-knyazev/

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).

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

  1. ↑ 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
  2. ↑ Knyazev's NSF awards
  3. ↑ 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
  4. ↑ Goodland, Marianne (6 May 1999), "President's Faculty Excellence Award for Advancing Teaching and Learning through Technology", Silver & Gold Record, XXIX (34)
  5. ↑ Professor Emeritus University of Colorado Denver, 6 January 2016
  6. ↑ Society for Industrial and Applied Mathematics (SIAM) Fellows Class of 2016, 31 March 2016
  7. ↑ American Mathematical Society (AMS) Fellows Class of 2019, 31 October 2018
  8. ↑ Andrew Knyazev moved to MERL, 2012
  9. ↑ Knyazev's Website at Mitsubishi Electric Research Laboratories Archived January 20, 2018, at the Wayback Machine
  10. ↑ Knyazev, A.V. (1998), "Preconditioned eigensolvers - an oxymoron?" (PDF), Electron. Trans. Numer. Anal., 7: 104–123
  11. ↑ 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
  12. ↑ 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
  13. ↑ 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
  14. ↑ 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
  15. ↑ 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
  16. ↑ 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
  17. ↑ 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
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