• SJSU Singular Matrix Database
  • Matrix group: GHS_indef
  • Click here for a description of the GHS_indef group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups

  • Matrix: GHS_indef/aug2d
  • Description: Gould, Hu, & Scott: expanded system-2D PDE (CUTEr)
  • download as a MATLAB mat-file, file size: 140 KB. Use SJget(326) or SJget('GHS_indef/aug2d') in MATLAB.
  • download in Matrix Market format, file size: 104 KB.
  • download in Rutherford/Boeing format, file size: 94 KB.


    A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

    Routine svds_err, version 1.0, used with Matlab (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab (R2008a) to calculate singular values 19206 to 19211 and associated error bounds.


    dmperm of GHS_indef/aug2d

    Matrix properties (click for a legend)  
    number of rows29,008
    number of columns29,008
    structural full rank?no
    structural rank19,208
    numerical rank 19,208
    dimension of the numerical null space9,800
    numerical rank / min(size(A))0.66216
    Euclidean norm of A 2.8281
    calculated singular value # 192080.044876
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 192092.3846e-024
    gap in the singular values at the numerical rank:
    singular value # 19208 / singular value # 19209
    calculated condition number-2
    # of blocks from dmperm2
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorN. Gould
    editorN. Gould
    kind2D/3D problem
    2D/3D problem?yes

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))248,374 293,219
    Cholesky flop count1.1e+007 1.5e+007
    nnz(L+U), no partial pivoting467,740 557,430
    nnz(V) for QR, upper bound nnz(L) for LU3,305,290 2,624,890
    nnz(R) for QR, upper bound nnz(U) for LU602,205 641,561

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.