• 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-30
  • Description: IBM TJ Watson, non-linear optimization
  • download as a MATLAB mat-file, file size: 227 KB. Use SJget(337) or SJget('Schenk_IBMNA/c-30') in MATLAB.
  • download in Matrix Market format, file size: 193 KB.
  • download in Rutherford/Boeing format, file size: 156 KB.


    Routine svd from Matlab (R2008a) used to calculate the singular values.


    Matrix properties (click for a legend)  
    number of rows5,321
    number of columns5,321
    structural full rank?yes
    structural rank5,321
    numerical rank 5,320
    dimension of the numerical null space1
    numerical rank / min(size(A))0.99981
    Euclidean norm of A 4.682e+006
    calculated singular value # 53209.7571e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 53212.2358e-007
    gap in the singular values at the numerical rank:
    singular value # 5320 / singular value # 5321
    calculated condition number2.0941e+013
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    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 5321-by-1

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))42,738 43,473
    Cholesky flop count6.6e+005 6.7e+005
    nnz(L+U), no partial pivoting80,155 81,625
    nnz(V) for QR, upper bound nnz(L) for LU2,101,593 1,255,261
    nnz(R) for QR, upper bound nnz(U) for LU3,049,880 3,297,434

    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.