Matrix: Nemeth/nemeth20

Description: Newton-Schultz iteration, Z_k+1=Z_k+(1/2)*(I-(Z_k)^2)*Z_k. This is Z_20

Nemeth/nemeth20 graph
(undirected graph drawing)


Nemeth/nemeth20

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  • Matrix group: Nemeth
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  • download as a MATLAB mat-file, file size: 7 MB. Use UFget(784) or UFget('Nemeth/nemeth20') in MATLAB.
  • download in Matrix Market format, file size: 6 MB.
  • download in Rutherford/Boeing format, file size: 5 MB.

    Matrix properties
    number of rows9,506
    number of columns9,506
    nonzeros971,870
    structural full rank?yes
    structural rank9,506
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?no
    positive definite?no

    authorK. Nemeth
    editorT. Davis
    date1999
    kindsubsequent theoretical/quantum chemistry problem
    2D/3D problem?no

    Notes:

    next: Nemeth/nemeth21 first: Nemeth/nemeth01
    

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD523,271
    Cholesky flop count2.9e+07
    nnz(L+U), no partial pivoting, with AMD1,037,036
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD535,537
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,095,923

    SVD-based statistics:
    norm(A)0.999379
    min(svd(A))0.452561
    cond(A)2.20827
    rank(A)9,506
    sprank(A)-rank(A)0
    null space dimension0
    full numerical rank?yes

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

    Nemeth/nemeth20 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.