Matrix: JGD_Trefethen/Trefethen_20000b

Description: Diagonal matrices with primes, Nick Trefethen, Oxford Univ.

JGD_Trefethen/Trefethen_20000b graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 1018 KB. Use UFget(2212) or UFget('JGD_Trefethen/Trefethen_20000b') in MATLAB.
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    Matrix properties
    number of rows19,999
    number of columns19,999
    structural full rank?yes
    structural rank19,999
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?yes

    authorN. Trefethen
    editorJ.-G. Dumas
    kindcombinatorial problem
    2D/3D problem?no


    Diagonal matrices with primes, Nick Trefethen, Oxford Univ.           
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,                  
    Problem 7 of the Hundred-dollar, Hundred-digit Challenge Problems,    
    SIAM News, vol 35, no. 1.                                             
    7. Let A be the 20,000 x 20,000 matrix whose entries are zero         
    everywhere except for the primes 2, 3, 5, 7, . . . , 224737 along the 
    main diagonal and the number 1 in all the positions A(i,j) with       
    |i-j| = 1,2,4,8, . . . ,16384.  What is the (1,1) entry of inv(A)?    
    Filename in JGD collection: Trefethen/trefethen_20000__19999_minor.sms

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD82,368,615
    Cholesky flop count6.9e+11
    nnz(L+U), no partial pivoting, with AMD164,717,231
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD173,742,045
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD188,532,302

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero

    JGD_Trefethen/Trefethen_20000b 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.