• SJSU Singular Matrix Database
  • Matrix group: HB
  • Click here for a description of the HB group.
  • Click here for a list of all matrices
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  • Matrix: HB/lap_25
  • Description: FINITE ELEMENT PROBLEM. LAPLACIAN ON A 5 BY 5 GRID.
  • download as a MATLAB mat-file, file size: 925 bytes. Use SJget(136) or SJget('HB/lap_25') in MATLAB.
  • download in Matrix Market format, file size: 646 bytes.
  • download in Rutherford/Boeing format, file size: 646 bytes.

    HB/lap_25

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

    HB/lap_25

    Matrix properties (click for a legend)  
    number of rows25
    number of columns25
    structural full rank?yes
    structural rank25
    numerical rank 16
    dimension of the numerical null space9
    numerical rank / min(size(A))0.64
    Euclidean norm of A 7.4641
    calculated singular value # 160.5359
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.2204e-014
    calculated singular value # 177.3946e-016
    gap in the singular values at the numerical rank:
    singular value # 16 / singular value # 17
    7.2471e+014
    calculated condition number3.5481e+017
    condestInf
    nonzeros169
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typebinary
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorI. Duff
    editorI. Duff, R. Grimes, J. Lewis
    date1980
    kindstructural problem
    2D/3D problem?yes
    SJid136
    UFid1,177

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))138 131
    Cholesky flop count8.7e+002 7.4e+002
    nnz(L+U), no partial pivoting251 237
    nnz(V) for QR, upper bound nnz(L) for LU153 154
    nnz(R) for QR, upper bound nnz(U) for LU238 234

    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.