Andrei Knyazev (mathematician)

Andrei (Andrew) Knyazev

Andrew Knyazev
Born 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)

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 Дъяконов) 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, he 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. In 2012, he took a research position at the Mitsubishi Electric Research Laboratories.[3]

Knyazev was mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly the iterative method LOBPCG.[4] 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.[5][6]

Knyazev collaborated with John Osborn [7] on the theory of the Rayleigh–Ritz method (see also [8]) 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.[9] His Erdős number = 4.

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 moved to MERL, 2012
  4. ↑ 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
  5. ↑ wfoptalg variable ABINIT ver. 7.0
  6. ↑ 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
  7. ↑ 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
  8. ↑ 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
  9. ↑ 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

External links