• SJSU Singular Matrix Database
  • 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: 134 KB. Use SJget(315) or SJget('Muite/Chebyshev2') in MATLAB.
  • download in Matrix Market format, file size: 199 KB.
  • download in Rutherford/Boeing format, file size: 177 KB.

    Muite/Chebyshev2

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

    Muite/Chebyshev2

    Matrix properties (click for a legend)  
    number of rows2,053
    number of columns2,053
    structural full rank?yes
    structural rank2,053
    numerical rank 2,051
    dimension of the numerical null space2
    numerical rank / min(size(A))0.99903
    Euclidean norm of A 20277
    calculated singular value # 20511.0002e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.4688e-009
    calculated singular value # 20523.8431e-012
    gap in the singular values at the numerical rank:
    singular value # 2051 / singular value # 2052
    2.6025e+006
    calculated condition number5.6203e+015
    condest6.7136e+016
    nonzeros18,447
    # 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
    SJid315
    UFid1,865

    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 18,832
    Cholesky flop count1.0e+005 1.7e+005
    nnz(L+U), no partial pivoting26,641 35,611
    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 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.