• SJSU Singular Matrix Database
• Matrix group: Regtools
• Click here for a description of the Regtools group.
• Click here for a list of all matrices
• Click here for a list of all matrix groups

• Matrix: Regtools/ursell_100
• Description: URSELL 100x100 Test problem: integral equation with no square integrable solution.
• download as a MATLAB mat-file, file size: 10 KB. Use SJget(257) or SJget('Regtools/ursell_100') in MATLAB.
• download in Matrix Market format, file size: 22 KB.
• download in Rutherford/Boeing format, file size: 6 KB.

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

 Matrix properties (click for a legend) number of rows 100 number of columns 100 structural full rank? yes structural rank 100 numerical rank 98 dimension of the numerical null space 2 numerical rank / min(size(A)) 0.98 Euclidean norm of A 0.5362 calculated singular value # 98 1.7205e-014 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 1.1102e-014 calculated singular value # 99 7.0092e-015 gap in the singular values at the numerical rank: singular value # 98 / singular value # 99 2.4547 calculated condition number 9.3473e+013 condest 2.4844e+014 nonzeros 10,000 # of blocks from dmperm 1 # strongly connected comp. 1 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? yes positive definite? no

 author Ursell editor Per Christian Hansen date 1974 kind ill-posed problem 2D/3D problem? no SJid 257 UFid -

 Additional fields size and type b full 100-by-1

Notes:

```    Constructed by the call [A,b]= ursell(100)

where ursell is from Regularization Tools. The description of
ursell from http://www2.imm.dtu.dk/~pch/Regutools/ is:

[A,b] = ursell(n)

Discretization of a first kind Fredholm integral equation with
kernel K and right-hand side g given by
K(s,t) = 1/(s+t+1) ,  g(s) = 1 ,
where both integration itervals are [0,1].

Note: this integral equation has NO square integrable solution.svals = svd(A);
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 5,050 5,050 Cholesky flop count 3.4e+005 3.4e+005 nnz(L+U), no partial pivoting 10,000 10,000 nnz(V) for QR, upper bound nnz(L) for LU 5,050 5,050 nnz(R) for QR, upper bound nnz(U) for LU 5,050 5,050

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.