Matrices contributed by The Mathworks, Inc.
Some matrices come from other sources.
pivtol: A small matrix from the spline toolbox that illustrates the dramatic
growth factor that can occur with a pivot tolerance of 0.1 (in
UMFPACK v4.0). Needs a tolerance of 0.26, for off-diagonal pivoting.
Pd: An unsymmetric matrix (x=P\d) with many sparse right-hand-sides. The Pd.A
matrix is 8081-by-8081. Pd.b and Pd_rhs.A are the same 8081-by-12406 matrix
(the right-hand-sides). It is highly reducible to block triangular form,
with 7877 diagonal blocks, the largest of which is 30-by-30. Only 9 of
the blocks are bigger than 1-by-1. This is a good candidate for a solver
based on dmperm.
Harvard500: Web connectivity matrix from Cleve Moler
(Numerical Computing with MATLAB, 2004). A(i,j) is nonzero if there
is a link from page j to page i. The URL of page j is in Problem.url{j}
in the MATLAB form of this problem. For more details, see Cleve Moler's
book at http://www.mathworks.com/moler . The matrix is 500-by-500, with
a structural rank of 233 and numerical rank of 170.
tomography: An earth science problem from David Yang. Contributed by
Bobby Cheng. Much like a medical tomography problem. "UMFPACK 4.0
is consistently slower than MATLAB v5." In MATLAB 7.1,
[L,U,P] = lu (A) takes 0.07 seconds (using GPLU), but UMFPACK v4.3 with
[L,U,P,Q] = lu (A) takes 0.11 seconds.
Kuu, Muu: symmetric positive definite matrices which caused problems with
UMFPACK v4.0 (in MATLAB 6.5). chol, or UMFPACK v4.3 or later, work fine.