• SJSU Singular Matrix Database
• Matrix group: Muite

• Matrix: Muite/Chebyshev1
• Description: Integration matrix, Chebyshev method, 4th order semilinear initial BVP
• download as a MATLAB mat-file, file size: 17 KB. Use SJget(279) or SJget('Muite/Chebyshev1') in MATLAB.

Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

 Matrix properties (click for a legend) number of rows 261 number of columns 261 structural full rank? yes structural rank 261 numerical rank 259 dimension of the numerical null space 2 numerical rank / min(size(A)) 0.99234 Euclidean norm of A 20277 calculated singular value # 259 1.7625e-005 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 9.4951e-010 calculated singular value # 260 3.6122e-012 gap in the singular values at the numerical rank: singular value # 259 / singular value # 260 4.8793e+006 calculated condition number 6.6931e+015 condest 7.5406e+016 nonzeros 2,319 # of blocks from dmperm 1 # strongly connected comp. 1 entries not in dmperm blocks 0 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 SJid 279 UFid 1,864

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: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 1,803 2,046 Cholesky flop count 1.3e+004 1.6e+004 nnz(L+U), no partial pivoting 3,345 3,831 nnz(V) for QR, upper bound nnz(L) for LU 1,293 1,293 nnz(R) for QR, upper bound nnz(U) for LU 34,191 34,191

Maintained by Leslie Foster, last updated 24-Apr-2009.

Entries 5 through 14 in the table of matrix properties and the singular
value plot were created using SJsingular code. The other plots
and statistics are produced using utilities from the SuiteSparse package.
Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.