Matrix: Nemeth/nemeth01

Description: Newton-Schultz iteration, Z_k+1=Z_k+(1/2)*(I-(Z_k)^2)*Z_k. This is Z_1

 (undirected graph drawing)

• Matrix group: Nemeth
• download as a MATLAB mat-file, file size: 5 MB. Use UFget(765) or UFget('Nemeth/nemeth01') in MATLAB.

 Matrix properties number of rows 9,506 number of columns 9,506 nonzeros 725,054 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 theoretical/quantum chemistry problem sequence 2D/3D problem? no

Notes:

```next: Nemeth/nemeth02 first: Nemeth/nemeth01
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 388,262 Cholesky flop count 1.6e+07 nnz(L+U), no partial pivoting, with AMD 767,018 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 397,712 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 865,722

 SVD-based statistics: norm(A) 43.0717 min(svd(A)) 0.307827 cond(A) 139.922 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

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.