Andrei Knyazev (mathematician)

Andrei (Andrew) Knyazev

Andrew Knyazev
Occupation Mathematician
Known for eigenvalue solvers

Andrei (Andrew) Knyazev is a Russian-American mathematician. He graduated from the Moscow State University under the supervision of Evgenii Georgievich D'yakonov in 1981 and obtained his PhD in Numerical Mathematics at the Russian Academy of Sciences under the supervision of Vyacheslav Ivanovich Lebedev in 1985. Since 1994, he is Professor of Mathematics at the University of Colorado Denver. His research has been supported by NSF and DOE grants since 1995.

Knyazev is mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly the iterative method LOBPCG.[1] An implementation of LOBPCG is available in the public software package BLOPEX, maintained by Knyazev. The LOBPCG has been also implemented in a popular public electronic structure calculations package ABINIT.[2]

Back in the Soviet Union, Knyazev has collaborated with Bakhvalov on numerical solution of elliptic partial differential equations (PDE's) with large jumps in the main coefficients.[3] Knyazev has also contributed to the theory of the Rayleigh–Ritz method.[4]

References

  1. ^ 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 
  2. ^ 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 
  3. ^ Bakhvalov, N.S.; Knyazev, A.V.; Parashkevov, R.R. (2002), "Extension Theorems for Stokes and Lame 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 
  4. ^ 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 

External links