Eigenvalue Project

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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.

Contents

Current status

The group leader, Andrew Knyazev, has moved to MERL as of Fall 2012.

Major results

  • The BLOPEX software has been developed for solving eigenvalue problems

Members

Group Leader

Andrew Knyazev

Professor Andrew Knyazev

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.

Former Ph.D. students

  • Donald McCaun, graduated fall 2012, works on BLOPEX, image segmentation, and gene clustering.
Donald McCaun
Affimetrix DNA Microarray
  • 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.
Peizhen Zhu
3D majorization example
Eugene Vecharynski
Preconditioned Eigensolver
Ilya Lashuk
AMG Element Agglomeration
Abram Jujunashvili
Subspaces
Merico Argentati
Matrix Applications

Former master students

David Duran
Molecular Dynamics

Former undergraduate students

  • Andrew Dougherty 2011-2012 UROP grant winner. Testing BLOPEX with different LINUX compilers and works on image segmentation.
Andrew Dougherty
  • 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.
Manuchehr Aminian
3D image segmentation

Latest Funding

  • 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

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