Matrix: Nemeth/nemeth03
Description: Newton-Schultz iteration, Z_k+1=Z_k+(1/2)*(I-(Z_k)^2)*Z_k. This is Z_3
(undirected graph drawing) |
Matrix properties | |
number of rows | 9,506 |
number of columns | 9,506 |
nonzeros | 394,808 |
structural full rank? | yes |
structural rank | 9,506 |
# of blocks from dmperm | 1 |
# strongly connected comp. | 1 |
explicit zero entries | 0 |
nonzero pattern symmetry | symmetric |
numeric value symmetry | symmetric |
type | real |
structure | symmetric |
Cholesky candidate? | no |
positive definite? | no |
author | K. Nemeth |
editor | T. Davis |
date | 1999 |
kind | subsequent theoretical/quantum chemistry problem |
2D/3D problem? | no |
Notes:
next: Nemeth/nemeth04 first: Nemeth/nemeth01
Ordering statistics: | result |
nnz(chol(P*(A+A'+s*I)*P')) with AMD | 226,880 |
Cholesky flop count | 5.4e+06 |
nnz(L+U), no partial pivoting, with AMD | 444,254 |
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 234,871 |
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 459,637 |
SVD-based statistics: | |
norm(A) | 0.164743 |
min(svd(A)) | 0.154444 |
cond(A) | 1.06668 |
rank(A) | 9,506 |
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.