Matrix: JGD_Trefethen/Trefethen_300

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

 (undirected graph drawing)

• Home page of the UF Sparse Matrix Collection
• Matrix group: JGD_Trefethen
• Click here for a description of the JGD_Trefethen group.
• Click here for a list of all matrices
• Click here for a list of all matrix groups
• download as a MATLAB mat-file, file size: 9 KB. Use UFget(2208) or UFget('JGD_Trefethen/Trefethen_300') in MATLAB.
• download in Matrix Market format, file size: 8 KB.
• download in Rutherford/Boeing format, file size: 7 KB.

 Matrix properties number of rows 300 number of columns 300 nonzeros 4,678 structural full rank? yes structural rank 300 # 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_300.sms
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 20,230 Cholesky flop count 2.2e+06 nnz(L+U), no partial pivoting, with AMD 40,160 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 32,715 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 40,769

 SVD-based statistics: norm(A) 1987.27 min(svd(A)) 1.12105 cond(A) 1772.69 rank(A) 300 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 (A)) ; 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.