Matrix: Muite/Chebyshev2

Description: Integration matrix, Chebyshev method, 4th order semilinear initial BVP

Muite/Chebyshev2 graph Muite/Chebyshev2 graph
(bipartite graph drawing) (graph drawing of A+A')


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  • Matrix group: Muite
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  • download as a MATLAB mat-file, file size: 119 KB. Use UFget(1865) or UFget('Muite/Chebyshev2') in MATLAB.
  • download in Matrix Market format, file size: 198 KB.
  • download in Rutherford/Boeing format, file size: 176 KB.

    Matrix properties
    number of rows2,053
    number of columns2,053
    structural full rank?yes
    structural rank2,053
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 50%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 2053-by-1


    Chebyshev integration matrix from Benson Muite, Oxford.  Details of the  
    matrices can be found in a preprint at  
    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:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD14,347
    Cholesky flop count1.0e+05
    nnz(L+U), no partial pivoting, with AMD26,641
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD8,208
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD2,108,431

    SVD-based statistics:
    null space dimension2
    full numerical rank?no
    singular value gap2.65179e+06

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    Muite/Chebyshev2 svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.