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

  • Matrix: Schenk_IBMNA/c-56
  • Description: IBM TJ Watson, non-linear optimization
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(435) or SJget('Schenk_IBMNA/c-56') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.


    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 35902 to 35907 and associated error bounds.


    dmperm of Schenk_IBMNA/c-56

    Matrix properties (click for a legend)  
    number of rows35,910
    number of columns35,910
    structural full rank?yes
    structural rank35,910
    numerical rank 35,904
    dimension of the numerical null space6
    numerical rank / min(size(A))0.99983
    Euclidean norm of A 1.207e+005
    calculated singular value # 359048.2953e-006
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 359051e-008
    gap in the singular values at the numerical rank:
    singular value # 35904 / singular value # 35905
    calculated condition number-2
    # of blocks from dmperm5
    # strongly connected comp.5
    entries not in dmperm blocks12
    explicit zero entries660
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    editorO. Schenk
    kindoptimization problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 35910-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))629,137 586,705 572,873
    Cholesky flop count7.3e+007 4.9e+007 4.4e+007
    nnz(L+U), no partial pivoting1,222,364 1,137,500 1,109,848
    nnz(V) for QR, upper bound nnz(L) for LU11,617,211 7,686,999 7,026,215
    nnz(R) for QR, upper bound nnz(U) for LU19,148,275 17,817,746 17,039,113

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 660 explicit zero entries.

    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.