**Email: **andrew.knyazev@ucdenver.edu**Website: **http://math.ucdenver.edu/~aknyazev/**Office Location: **AB1, Suite 4000**Phone:** (303) 315-1700 (front desk)**Office hours: **by appointment**Areas of Expertise:**Computational and Applied Mathematics

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

**Awards**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.

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.

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

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