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


  • Matrix: HB/saylr3
  • Description: UNSYMMETRIC MATRIX OF PAUL SAYLOR - 10 BY 10 BY 10 3D GRID MAY, 1983
  • download as a MATLAB mat-file, file size: 15 KB. Use SJget(216) or SJget('HB/saylr3') in MATLAB.
  • download in Matrix Market format, file size: 11 KB.
  • download in Rutherford/Boeing format, file size: 9 KB.

    HB/saylr3

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    HB/saylr3

    dmperm of HB/saylr3

    Matrix properties (click for a legend)  
    number of rows1,000
    number of columns1,000
    structural full rank?yes
    structural rank1,000
    numerical rank 998
    dimension of the numerical null space2
    numerical rank / min(size(A))0.998
    Euclidean norm of A 5.0449
    calculated singular value # 9980.00032349
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    8.8818e-013
    calculated singular value # 9991.2142e-016
    gap in the singular values at the numerical rank:
    singular value # 998 / singular value # 999
    2.6643e+012
    calculated condition numberInf
    condestInf
    nonzeros3,750
    # of blocks from dmperm318
    # strongly connected comp.318
    entries not in dmperm blocks6
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?no
    positive definite?no

    authorR. Kendall, D. Peaceman, H. Stone, W. Watts
    editorP. Saylor
    date1984
    kindcomputational fluid dynamics problem
    2D/3D problem?yes
    SJid216
    UFid240

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))9,590 10,249 9,586
    Cholesky flop count2.5e+005 2.7e+005 2.5e+005
    nnz(L+U), no partial pivoting18,180 19,498 18,178
    nnz(V) for QR, upper bound nnz(L) for LU17,636 18,079 18,308
    nnz(R) for QR, upper bound nnz(U) for LU32,079 32,914 33,055

    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.