Matrix: JGD_Trefethen/Trefethen_200b

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

 (undirected graph drawing)

• Matrix group: JGD_Trefethen
• download as a MATLAB mat-file, file size: 6 KB. Use UFget(2206) or UFget('JGD_Trefethen/Trefethen_200b') in MATLAB.

 Matrix properties number of rows 199 number of columns 199 nonzeros 2,873 structural full rank? yes structural rank 199 # 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_200__199_minor.sms
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 8,720 Cholesky flop count 6.0e+05 nnz(L+U), no partial pivoting, with AMD 17,241 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 13,770 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 17,885

 SVD-based statistics: norm(A) 1223.37 min(svd(A)) 2.34439 cond(A) 521.829 rank(A) 199 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