Matrix: Castrillon/denormal

Description: denormals in A+alpha*I as alpha > 0 varies, J. Castrillon, Teledyne

Castrillon/denormal graph
(undirected graph drawing)


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  • Matrix group: Castrillon
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  • download as a MATLAB mat-file, file size: 1 MB. Use UFget(1892) or UFget('Castrillon/denormal') in MATLAB.
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    Matrix properties
    number of rows89,400
    number of columns89,400
    structural full rank?yes
    structural rank89,400
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?yes

    authorJ. Castrillon
    editorT. Davis
    kindcounter-example problem
    2D/3D problem?no


    The problem is x=(A+alpha*I)\b as alpha varies from 0 to 100.  However,
    as this occurs, performance suffers because of the many denormals that 
    appear below the diagonal in L.                                        

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD8,231,641
    Cholesky flop count2.5e+09
    nnz(L+U), no partial pivoting, with AMD16,373,882
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD16,686,436
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD30,789,903

    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.