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University of Colorado Denver College of Liberal Arts and Sciences

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Faculty & Staff Directory

Andrew Knyazev, Ph.D.


Office Location: AB1, Suite 4000
Phone: (303) 315-1700 (front desk)
Office hours: by appointment
Areas of Expertise:
Computational and Applied Mathematics


Education & Degrees

Ph.D., Numerical Mathematics, Ph.D. Institute of Numerical Mathematics Russian Academy of Sciences, 1985

B.A. & M.S., Computer Science and Cybernetics, Moscow State University, 1981


Math Department, University of Colorado Denver: Professor, 2009-present; Associate Professor, 1994-2009

Courant Institute of Mathematical Sciences, New York University: Visiting Researcher, 1992-1994

Institute of Numerical Mathematics Russian Academy of Sciences: Senior Scientist, 1983-1992

Moscow Physico-Technical Institute (Moscow Institute of Physics and Technology), FPFE, Assistant Professor, 1985-1991

Moscow State University, Dept. Mathematics and Mechanics: Instructor, 1986-1988

Moscow Institute of Engineering and Physics: Instructor, 1982-1985

Kurchatov's Institute of Atomic Energy, Nuclear Reactors: Software Engineer, 1981-1983

Excellence in Research Award University of Colorado Denver, 2008

Teaching Excellence Award for the College of Liberal Arts and Sciences at the University of Colorado Denver, 2000

Faculty Research Fellowship, University of Colorado Denver, 2000

Researcher/Creative Artist Award for the College of Liberal Arts and Sciences at the University of Colorado Denver, 1999

UC Denver nominee for the University of Colorado President's Faculty Excellence Award for Advancing Teaching and Learning through Technology, 1999

Research Interests
numerical linear algebra, iterative solution of large sparse linear systems and eigenproblems, bounds for eigenvalues; numerical solution of partial differential equations, homogenization, numerical methods in linear elasticity, domain decomposition, embedding and multigrid methods, finite element methods; parallel computation, software development; electronic structure calculations in nanosciences; spectral clustering in data mining and information retrieval, spectral image segmentation and graph partitioning; clustering of DNA microarray and tiling array data.

Select Publications

D'yakonov, E. G.; Knyazev, A. V. A group iteration method for finding the lowest eigenvalues. (Russian) Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1982, no. 2, 29--34, 81.

Knyazev, A. V. "Convergence rate estimates for iterative methods for a mesh symmetric eigenvalue problem." Soviet J. Numer. Anal. Math. Modelling 2 (1987), no. 5, 371--396.

N. S. Bakhvalov and A. V. Knyazev, "Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components," In Numerical Methods and Applications, Ed. Gury I. Marchuk, CRC Press, 221-276, 1994.

A. V. Knyazev, "Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method." SIAM Journal on Scientific Computing 23 (2001), no. 2, pp. 517-541.

N. S. Bakhvalov, A. V. Knyazev, and R. R. Parashkevov, "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, 9 (2002) no. 2, 115-139.

A. V. Knyazev and Olof Widlund, Lavrentiev "Regularization + Ritz Approximation = Uniform Finite Element Error Estimates for Differential Equations with Rough Coefficients." Mathematics of Computation, 72 (2003), 17-40.

A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov, "Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc" (2007). SIAM Journal on Scientific Computing (SISC). 25(5): 2224-2239,

F. Bottin, S. Leroux, A. Knyazev, G. Zerah, "Large scale ab initio calculations based on three levels of parallelization." (2008). Computational Material Science, 42(2), 329-336.

A. V. Knyazev and M. E. Argentati, "Rayleigh-Ritz majorization error bounds with applications to FEM," (2010). SIAM. J. Matrix Anal. & Appl. Volume 31, Issue 3, pp. 1521-1537.

A. V. Knyazev, A. Jujunashvili, and M. E. Argentati, "Angles Between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods" (2010). Journal of Functional Analysis, 259 pp. 1323-1345.

Courses Taught

MATH 3200: Elementary Differential Equations
MATH 3191: Linear Algebra
MATH 4650 and C SC 4656: Numerical Analysis I
MATH 5660: Numerical Analysis I
MATH 5667: Approximation Theory
MATH 7132: Functional Analysis
MATH 8660: Math Finite Elmntl Mthds
MATH 8664: Iterative Methods in Numerical Linear Algebra