• 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/finance256
  • Description: Gould, Hu, & Scott: linear programming problem from Pothen & Kumfert
  • download as a MATLAB mat-file, file size: 441 KB. Use SJget(468) or SJget('GHS_psdef/finance256') in MATLAB.
  • download in Matrix Market format, file size: 441 KB.
  • download in Rutherford/Boeing format, file size: 349 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 35820 to 35825 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows37,376
    number of columns37,376
    structural full rank?yes
    structural rank37,376
    numerical rank 35,822
    dimension of the numerical null space1,554
    numerical rank / min(size(A))0.95842
    Euclidean norm of A 13.742
    calculated singular value # 358220.00030127
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 358231.0488e-013
    gap in the singular values at the numerical rank:
    singular value # 35822 / singular value # 35823
    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

    authorA. Berger, J. Mulvey, E. Rothberg, R. Vanderbei
    editorN. Gould, Y. Hu, J. Scott
    kindoptimization problem
    2D/3D problem?no

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))1,704,398 872,553
    Cholesky flop count6.2e+008 6.9e+007
    nnz(L+U), no partial pivoting3,371,420 1,707,730
    nnz(V) for QR, upper bound nnz(L) for LU3,628,213 3,268,094
    nnz(R) for QR, upper bound nnz(U) for LU7,857,994 7,700,446

    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.