• 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
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  • Matrix: Schenk_IBMNA/c-64
  • Description: Olaf Schenk, Univ. Basel: IBM TJ Watson, Yorktown, nonlinear optimization
  • download as a MATLAB mat-file, file size: 5 MB. Use SJget(469) or SJget('Schenk_IBMNA/c-64') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 3 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 with opts.tol_eigs = 1e-008, used with Matlab (R2008a) to calculate singular values 50939 to 50944 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows51,035
    number of columns51,035
    structural full rank?yes
    structural rank51,035
    numerical rank 50,941
    dimension of the numerical null space94
    numerical rank / min(size(A))0.99816
    Euclidean norm of A 2.0654e+006
    calculated singular value # 509411.1988e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 509421.1755e-005
    gap in the singular values at the numerical rank:
    singular value # 50941 / singular value # 50942
    calculated condition number-2
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries9,856
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 51035-by-1


    next: Schenk_IBMNA/c-64b first: Schenk_IBMNA/c-64

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))714,790 827,956
    Cholesky flop count5.1e+007 6.6e+007
    nnz(L+U), no partial pivoting1,378,545 1,604,877
    nnz(V) for QR, upper bound nnz(L) for LU61,293,356 -
    nnz(R) for QR, upper bound nnz(U) for LU114,502,548 -

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 9856 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.