Matrix: JGD_Trefethen/Trefethen_20b

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

JGD_Trefethen/Trefethen_20b graph
(undirected graph drawing)


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  • Matrix group: JGD_Trefethen
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  • download as a MATLAB mat-file, file size: 1 KB. Use UFget(2203) or UFget('JGD_Trefethen/Trefethen_20b') in MATLAB.
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    Matrix properties
    number of rows19
    number of columns19
    structural full rank?yes
    structural rank19
    # 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_20__19_minor.sms     

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD128
    Cholesky flop count1.0e+03
    nnz(L+U), no partial pivoting, with AMD237
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD155
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD188

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

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

    JGD_Trefethen/Trefethen_20b 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.