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

  • Matrix: Gaertner/nopoly
  • Description: Structuresymmetric Matrix nopoly K. Gaertner ETH Zurich Jan 1998.
  • download as a MATLAB mat-file, file size: 138 KB. Use SJget(356) or SJget('Gaertner/nopoly') in MATLAB.
  • download in Matrix Market format, file size: 141 KB.
  • download in Rutherford/Boeing format, file size: 112 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 10771 to 10774 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows10,774
    number of columns10,774
    structural full rank?yes
    structural rank10,774
    numerical rank 10,773
    dimension of the numerical null space1
    numerical rank / min(size(A))0.99991
    Euclidean norm of A 23.244
    calculated singular value # 107730.00028689
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 107749.8596e-015
    gap in the singular values at the numerical rank:
    singular value # 10773 / singular value # 10774
    calculated condition number2.3575e+015
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorK. Gaertner
    editorF. Grund
    kindundirected weighted graph
    2D/3D problem?no

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))163,985 167,016
    Cholesky flop count4.6e+006 4.4e+006
    nnz(L+U), no partial pivoting317,196 323,258
    nnz(V) for QR, upper bound nnz(L) for LU222,086 244,670
    nnz(R) for QR, upper bound nnz(U) for LU423,762 462,725

    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.