Matrix properties
number of rows	4,101
number of columns	4,101
nonzeros	36,879
structural full rank?	yes
structural rank	4,101
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	50%
numeric value symmetry	0%
type	real
structure	unsymmetric
Cholesky candidate?	no
positive definite?	no

author	B. Muite
editor	T. Davis
date	2007
kind	structural problem
2D/3D problem?	yes

Notes:

Chebyshev integration matrix from Benson Muite, Oxford.  Details of the  
matrices can be found in a preprint at http://www.maths.ox.ac.uk/~muite  
entitled "A comparison of Chebyshev methods for solving fourth-order     
semilinear initial boundary value problems," June 2007.   These matrices 
are very ill-conditioned, partly because of the dense rows which are hard
to scale when coupled with the rest of the matrix.                       

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	28,683
Cholesky flop count	2.0e+05
nnz(L+U), no partial pivoting, with AMD	53,265
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	16,400
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	8,411,151

SVD-based statistics:
norm(A)	2.01756e+06
min(svd(A))	3.33757e-12
cond(A)	6.04502e+17
rank(A)	4,099
sprank(A)-rank(A)	2
null space dimension	2
full numerical rank?	no
singular value gap	168166

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.