Software and codes for matrix computations

       If you cannot access any code or if you need other codes from our research, please email us.

• SuperDC (NEW)
  Stable and superfast divide-and-conquer eigenvalue decomposition: link
• FMM1D (NEW)
  Stable 1D FMM and triangular FMM: link
• Collection of test codes for structured matrix computations:
  Structured Matrix Market
• Fast local factorization update for elliptic PDEs
  Matlab codes
  Reference: X. Liu, J. Xia, and M. V. de Hoop, Fast factorization update for general elliptic equations under multiple coefficient updates,
  SIAM J. Sci. Comput., 42 (2020), pp. A1174-1199. (PDF. Journal article link)
• Interconnected hierarchical structures
  Matlab codes
  Reference: X. Liu, J. Xia, M. V. de Hoop, and X. Ou, A fast direct elliptic solver via interconnected hierarchical structures, preprint, (2020).
• Robust rank structured preconditioners for SPD matrices: One version
  Based on reference:
  Xia and Z. Xin, Effective and robust preconditioning of general SPD matrices via structured incomplete factorization, SIAM J. Matrix Anal. Appl., 38 (2017), pp. 1298-1322.
• A superfast and stable Toeplitz direct solver via randomization and hierarchically semiseparable (HSS) methods
  Fortran codes -- be sure to check the file README first
  Based on these papers:
  1. J. Xia, Y. Xi, and M. Gu, A superfast structured solver for Toeplitz linear systems via randomized sampling,
  SIAM J. Matrix Anal. Appl., 33 (2012), pp. 837-858. (PDF. Journal article link)
  2. Y. Xi, J. Xia, S. Cauley, and V. Balakrishnan, Superfast and stable structured solvers for Toeplitz least squares via randomized sampling,
  SIAM J. Matrix Anal. Appl., 35 (2014), pp. 44-72. (PDF. Journal article link)
  3. X. Liu, J. Xia, and M. V. de Hoop, Parallel randomized and matrix-free direct solvers for large structured dense linear systems,
  SIAM J. Sci. Comput., 38 (2016), S508-S538. (PDF. Journal article link)
• A hierarchically semiseparable (HSS) package
  Matlab codes
  Reference:
  J. Xia, S. Chandrasekaran, M. Gu, X. S. Li, Fast algorithms for hierarchically semiseparable matrices,
  Numer. Linear Algebra Appl., 17 (2010), pp. 953-976.
• SuperMF: O(n) cost 2D and O(n^{4/3}) cost 3D direct PDE solver and black-box sparse solver
  Fortran 90 codes (zip file); Matlab codes (zip file). Please email.
• A fast O(n^2) time QR eigensolver for companion matrices/polynomials
  Fortran 90 codes (zip file). With J. Zhu.
  Driver routine: driver.f90.
  Required packages: LAPACK, BLAS, and MPFUN (necessary files included).
  Used for the paper:
   "A Fast Eigensolver for Companion Matrices"
    S. Chandrasekaran, M. Gu, J. Xia, and J, Zhu, Oper. Theory Adv. Appl., Birkhauser Basel, 179 (2008), pp. 111-143.
• Superfast SSS Toeplitz solver -- outdated; please refer to the HSS version above
  Fortran 90 codes (zip file). With J. Zhu.
  Driver routine: driver1.f90.
  Required packages: LAPACK with BLAS.
  Used for the paper:
   "A Superfast Algorithm for Toeplitz Systems of Linear Equations"
    S. Chandrasekaran, M. Gu, X. Sun, J. Xia, and J, Zhu., to appear, SIAM J. Matrix Anal. Appl.
• A low-rank update eigensolver
  Fortran 90 codes. For the paper:
  " Low-Rank Update Eigensolver for Supercell Band Structure Calculations",
  M. Gu, B. Parlett, D. Ting, J. Xia, J. Comput. Electron. 1(2002), pp. 411-414.
• Codes for statistical condition estimations of linear systems and eigenproblems