• UF Sparse Matrix Collection
  • Matrix group: Muite
  • Click here for a description of the Muite group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups


  • Matrix: Muite/Chebyshev2
  • Description: Integration matrix, Chebyshev method, 4th order semilinear initial BVP
  • download as a MATLAB mat-file, file size: 119 KB. Use UFget(1865) or UFget('Muite/Chebyshev2') in MATLAB.
  • download in Matrix Market format
  • download in Rutherford/Boeing format

    Muite/Chebyshev2

    Muite/Chebyshev2 graph

    Matrix properties
    number of rows2,053
    number of columns2,053
    nonzeros18,447
    structural full rank?yes
    structural rank2,053
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 50%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorB. Muite
    editorT. Davis
    date2007
    kindstructural problem
    2D/3D problem?yes

    Additional fieldssize and type
    bfull 2053-by-1

    Notes:

    Chebyshev integration matrix from Benson Muite, Oxford.  Details of the  
    matrices can be found in a preprint at http://www.maths.ox.ac.uk/~muite  
    entitled "A comparison of Chebyshev methods for solving fourth-order     
    semilinear initial boundary value problems," June 2007.   These matrices 
    are very ill-conditioned, partly because of the dense rows which are hard
    to scale when coupled with the rest of the matrix.                       
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))14,347 18,822
    Cholesky flop count1.0e+05 1.7e+05
    nnz(L+U), no partial pivoting26,641 35,591
    nnz(V) for QR, upper bound nnz(L) for LU10,253 10,253
    nnz(R) for QR, upper bound nnz(U) for LU2,108,431 2,108,431

    Maintained by Tim Davis, last updated 04-May-2008.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.