Description: Ill-conditioned matrix from a Stokes problem, by Dominick Szczerba
|(bipartite graph drawing)||(graph drawing of A+A')|
|number of rows||20,896|
|number of columns||20,896|
|structural full rank?||yes|
|# of blocks from dmperm||1|
|# strongly connected comp.||1|
|explicit zero entries||0|
|nonzero pattern symmetry||99%|
|numeric value symmetry||33%|
|kind||computational fluid dynamics problem|
|Additional fields||size and type|
The matrix comes from a global formulation of the Stokes problem posed directly (without pressure correction) on an unstructured tet mesh. It includes momentum equations (3 quadrants) and continuity equation (last quadrant). Unknowns are organized as : vx, vy, vz, p. The last quadrant does not contain diagonal entries of course (continuity eq. does not contain pressure) and is the reason bicgstab and related methods do not work. Does not invert nicely with umfpack (strong oscillations in the 4th quadrant of the solution). LSQR produces better results (smaller oscillations) but takes ages. Dominik Szczerba, Ph.D. Computer Vision Lab, ETH. CH-8092 Zurich. http://www.vision.ee.ethz.ch/~domi
|nnz(chol(P*(A+A'+s*I)*P')) with AMD||3,280,425|
|Cholesky flop count||2.1e+09|
|nnz(L+U), no partial pivoting, with AMD||6,539,954|
|nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD||7,800,780|
|nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD||13,814,174|
|null space dimension||0|
|full numerical rank?||yes|
|singular values (MAT file):||click here|
|SVD method used:||s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero|
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.