Matrix: JGD_Trefethen/Trefethen_20000

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

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 Matrix properties number of rows 20,000 number of columns 20,000 nonzeros 554,466 structural full rank? yes structural rank 20,000 # of blocks from dmperm 1 # strongly connected comp. 1 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type integer structure symmetric Cholesky candidate? yes positive definite? yes

 author N. Trefethen editor J.-G. Dumas date 2008 kind combinatorial problem 2D/3D problem? no

Notes:

```Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html

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)?

http://www.siam.org/news/news.php?id=388

Filename in JGD collection: Trefethen/trefethen_20000.sms
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 86,761,641 Cholesky flop count 7.4e+11 nnz(L+U), no partial pivoting, with AMD 173,503,282 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 171,632,676 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 187,325,442

 SVD-based statistics: norm(A) 224737 min(svd(A)) 1.12055 cond(A) 200559 rank(A) 20,000 sprank(A)-rank(A) 0 null space dimension 0 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 status: ok

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.