Matrix datasets

• Some matrices for generalized eigenvalue problems

  These matrices are from
  1. Adaptive finite element discretization of the Kohn-Sham equation in DFT calculations;
  2. Density functional tight binding (DFTB) calculations;
  3. Transmission eigenvalue problems .
  Some of the matrices (especially the DFTB ones) have highly clustered eigenvalue, some eigenvalues have very high multiplicities. Thus these matrices provide some interesting and challenging test problems for any eigen-solver.

• Some matrices from data mining applications

Some matlab code

• RSDFT (real-space density functional theory calculation package), to be posted
• CFGEIG (Chebyshev filtering for generalized eigenvalue problems), to be posted
• FPSVD/EVD (filtered partial SVD and EVD) [ download ]
• Block Chebyshev-Davidson with inner-outer restart code for hermitian eigenproblems
  [ download ]     The related paper is available here , with bibtex entry

  @Article{bchebdav,
    author =	 {Y. Zhou},
    title =	 {A block {Chebyshev-Davidson} method with inner-outer restart for large eigenvalue problems},
    journal =	 {J. Comput. Phys.},
    year =	 2010,
    volume =	 229,
    number =	 24,
    pages =	 {9188-9200},
  }
  

• Chebyshev-Davidson code for hermitian eigenproblems
  [ download ]     The related paper is available here , with bibtex entry

  @Article{chebdav,
    author =	 {Y. Zhou and Y. Saad},
    title =	 {A {Chebyshev-Davidson} Algorithm for Large Symmetric Eigenvalue Problems},
    journal =	 {SIAM J. Matrix Anal. Appl.},
    year =	 2007,
    volume =	 29,
    number =	 3,
    pages =	 {954-971}
  }
  

• Block Krylov-Schur code for hermitian eigenproblems: [ download ]     The related paper is available here .
• Generalized Davidson (RQI, Newton, and modified Jacobi-Davidson) for eigenvalue computations
  [ download ] The related paper is available here , with bibtex entry

  @Article{gdav-2006,
    author =	 {Y. Zhou},
    title =	 "Studies on Jacobi-Davidson, Rayleigh Quotient Iteration, Inverse Iteration Generalized Davidson, and Newton Updates",
    journal =	 {Numer. Linear Algebra Appl.},
    year =	 2006,
    volume =	 13,
    number =	 8,
    pages =	 {621-642}
  }
  

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Last modified:   Nov. 2015