Matrix: JGD_Trefethen/Trefethen_150
Description: Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
(undirected graph drawing) |
Matrix properties | |
number of rows | 150 |
number of columns | 150 |
nonzeros | 2,040 |
structural full rank? | yes |
structural rank | 150 |
# 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_150.sms
Ordering statistics: | result |
nnz(chol(P*(A+A'+s*I)*P')) with AMD | 6,053 |
Cholesky flop count | 3.5e+05 |
nnz(L+U), no partial pivoting, with AMD | 11,956 |
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 8,215 |
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 10,294 |
SVD-based statistics: | |
norm(A) | 863.591 |
min(svd(A)) | 1.12166 |
cond(A) | 769.922 |
rank(A) | 150 |
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.