Andrei Knyazev (mathematician)

Andrei (Andrew) Knyazev

Andrew Knyazev
Born (1959-06-09) June 9, 1959
Moscow, Soviet Union
Fields Numerical analysis, Applied Mathematics, Computer Science
Institutions Kurchatov Institute
Institute of Numerical Mathematics RAS
University of Colorado Denver
Mitsubishi Electric Research Laboratories
Alma mater Moscow State University
Doctoral advisor Vyacheslav Ivanovich Lebedev
Doctoral students see Andrei Knyazev at the Mathematics Genealogy Project
Known for eigenvalue solvers
Notable awards IEEE Senior Member (2013)
Professor Emeritus University of Colorado Denver (2016)

Andrei (Andrew) Knyazev (Russian: Андрей Владимирович Князев) is a Russian-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 in 1981-1983, and then to 1992 at the Institute of Numerical Mathematics (Russian: ru:Институт вычислительной математики РАН) of the Russian Academy of Sciences, headed by Gury Marchuk (Russian: Гурий Иванович Марчук).

In 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]

In 2012, Knyazev took a research position at the Mitsubishi Electric Research Laboratories (MERL).[6] His research at MERL was on algorithms for image and video processing, data sciences, optimal control, material sciences, and numerical simulation of complex phenomena, resulting in patents and publications.

Knyazev was mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly preconditioning [7] and the iterative method LOBPCG.[8] An implementation of LOBPCG was available in the public software package BLOPEX. A popular public electronic structure calculations package ABINIT used LOBPCG for wavefunction parallel optimization.[9][10]

Knyazev collaborated with John Osborn [11] on the theory of the Ritz method in the finite element method context and with Nikolai Sergeevich Bakhvalov (Russian: Николай Серге́евич Бахвалов) on numerical solution of elliptic partial differential equations (PDE's) with large jumps in the main coefficients.[12] Jointly with his Ph.D. students, Knyazev pioneered using majorization for bounds in the Rayleigh–Ritz method (see [13] and references there) and contributed to the theory of angles between flats. [14] [15]

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: 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
  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. ↑ Andrew Knyazev moved to MERL, 2012
  7. ↑ Knyazev, A.V. (1998), "Preconditioned eigensolvers - an oxymoron?" (PDF), Electron. Trans. Numer. Anal. (ETNA) 7: 104–123
  8. ↑ 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, doi:10.1137/S1064827500366124
  9. ↑ wfoptalg variable ABINIT ver. 7.0
  10. ↑ Bottin, F.; Leroux, S.; Knyazev, A.; Zerah, G. (2008), "Large scale ab initio calculations based on three levels of parallelization", Computational Material Science 42 (2): 329–336, doi:10.1016/j.commatsci.2007.07.019
  11. ↑ Knyazev, A.V.; Osborn, J. (2006), "New A Priori FEM Error Estimates for Eigenvalues", SIAM. J. Num. Anal. 43 (6): 2647–2667, doi:10.1137/040613044
  12. ↑ 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 2 (2): 115–139, doi:10.1002/nla.259
  13. ↑ 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, doi:10.1137/08072574X
  14. ↑ 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, doi:10.1137/060649070
  15. ↑ 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, doi:10.1016/j.jfa.2010.05.018

External links

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