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

  • Matrix: GHS_psdef/srb1
  • Description: Gould, Hu, & Scott: from Christian Damhaug
  • download as a MATLAB mat-file, file size: 769 KB. Use SJget(504) or SJget('GHS_psdef/srb1') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 812 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 9152 to 9157 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows54,924
    number of columns54,924
    structural full rank?yes
    structural rank54,924
    numerical rank 9,154
    dimension of the numerical null space45,770
    numerical rank / min(size(A))0.16667
    Euclidean norm of A 58.8
    calculated singular value # 91540.002699
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 91555.9212e-015
    gap in the singular values at the numerical rank:
    singular value # 9154 / singular value # 9155
    calculated condition number-2
    # 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

    authorC. Damhaug
    editorN. Gould, Y. Hu, J. Scott
    kindstructural problem
    2D/3D problem?yes

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))9,801,174 10,440,750
    Cholesky flop count3.0e+009 3.5e+009
    nnz(L+U), no partial pivoting19,547,424 20,826,576
    nnz(V) for QR, upper bound nnz(L) for LU18,591,978 16,967,586
    nnz(R) for QR, upper bound nnz(U) for LU36,881,058 32,149,866

    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.