Muite/Chebyshev3

Integration matrix, Chebyshev method, 4th order semilinear initial BVP
Name Chebyshev3
Group Muite
Matrix ID 1866
Num Rows 4,101
Num Cols 4,101
Nonzeros 36,879
Pattern Entries 36,879
Kind Structural Problem
Symmetric No
Date 2007
Author B. Muite
Editor T. Davis
Structural Rank 4,101
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 50%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
SVD Statistics
Matrix Norm 2.017564e+06
Minimum Singular Value 3.337566e-12
Condition Number 6.045017e+17
Rank 4,099
sprank(A)-rank(A) 2
Null Space Dimension 2
Full Numerical Rank? no
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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.