• SJSU Singular Matrix Database
  • Matrix group: Muite
  • Click here for a description of the Muite group.
  • Click here for a list of all matrices
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  • Matrix: Muite/Chebyshev3
  • Description: Integration matrix, Chebyshev method, 4th order semilinear initial BVP
  • download as a MATLAB mat-file, file size: 233 KB. Use SJget(332) or SJget('Muite/Chebyshev3') in MATLAB.
  • download in Matrix Market format, file size: 355 KB.
  • download in Rutherford/Boeing format, file size: 309 KB.

    Muite/Chebyshev3

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

    Muite/Chebyshev3

    Matrix properties (click for a legend)  
    number of rows4,101
    number of columns4,101
    structural full rank?yes
    structural rank4,101
    numerical rank 4,099
    dimension of the numerical null space2
    numerical rank / min(size(A))0.99951
    Euclidean norm of A 2.0176e+006
    calculated singular value # 40991.0001e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    9.5484e-007
    calculated singular value # 41006.8627e-011
    gap in the singular values at the numerical rank:
    singular value # 4099 / singular value # 4100
    1.4573e+005
    calculated condition number7.0298e+017
    condest6.7122e+020
    nonzeros36,879
    # 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
    SJid332
    UFid1,866

    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'))28,683 37,804
    Cholesky flop count2.0e+005 3.5e+005
    nnz(L+U), no partial pivoting53,265 71,507
    nnz(V) for QR, upper bound nnz(L) for LU20,493 20,493
    nnz(R) for QR, upper bound nnz(U) for LU8,411,151 8,411,151

    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.