We are working on preconditioned solvers for eigenvalue and singular value problems: develop corresponding software, work on the theoretical issues, and contribute to applications.
Gross cluster is used as a test supercomputer, to debug the codes and run test examples.
The group leader, Andrew Knyazev, has moved to MERL as of Fall 2012.
- The BLOPEX software has been developed for solving eigenvalue problems
Professor Andrew Knyazev
- Ph.D. in Numerical Mathematics, Ph.D. adviser V.I. Lebedev Institute of Numerical Mathematics Russian Academy of Sciences, 1985
- B.A. and M.S. in Computer Science and Cybernetics, M.S. adviser - E.G. D'yakonov, Moscow State University, Cybernetics and Computer Science 1981
- 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.
Former Ph.D. students
- Donald McCaun, graduated fall 2012, works on BLOPEX, image segmentation, and gene clustering.
- Peizhen Zhu, graduated fall 2012, is testing BLOPEX in CYGWIN, and has obtained novel results related to numerical computation of canonical correlations and the principal component analysis, using the majorization theory.
- Yaugen (Eugene) Vecharynski, CLAS Outstanding PhD Student award Spring 2011, Preconditioned iterative methods for linear systems, eigenvalue and singular value problems. Currently a postdoctoral researcher at the University of Minnesota in the group of Yousef Saad. Eugene has developed BLOPEX-MATLAB interface in complex arithmetic, and has been involved in research on singular value computations and iterative eigenvalue and linear systems solvers.
- Ilya Lashuk, CLAS Outstanding PhD Student award Fall 2007 On Preconditioning for Linear Equations and Eigenvalue Problems. Currently a scientific researcher at DOE, Lawrence Livermore National Laboratory, Center for Applied Scientific Computing.
- Abram Jujunashvili, 2005, Angles Between Infinite-Dimensional Subspaces. Currently works in the industry as a database developer.
- Merico Argentati, CLAS Outstanding PhD Student award Fall 2003, Principal Angles Between Subspaces as Related to Rayleigh Quotient and Raleigh Ritz Inequalities with Applications to Eigenvalue Accuracy and an Eigenvalue Solver. Retired, an adjunct faculty of our department.
Former master students
- David Duran, Use of LOBPCG in Normal Coordinate Analysis for Molecular Structures, MS Presentation by Dave Duran, 2002. Currently (2011) at Boulder Imaging.
Former undergraduate students
- Andrew Dougherty 2011-2012 UROP grant winner. Testing BLOPEX with different LINUX compilers and works on image segmentation.
- Manuchehr Aminian, UC Denver Undergraduate Outstanding Research and Creative Activities 2011 Award. Accepted (2011) to the PhD program at the University of North Carolina at Chapel Hill. Developed OCTAVE/MATLAB software for 3D image segmentation.
- NSF Award DMS 1115734, Parallel Preconditioned Eigenvalue and Singular Value Solvers, 2011-2014, $180,000
- NSF Award DMS 0612751, Locally Optimal Preconditioned Eigenvalue Solvers, 2006-2010, $249,542
- NSF Award DMS 0728941, Analysis of Microarray Gene Expression Data, 2007-2008, $99,973