• SJSU Singular Matrix Database
• Matrix group: Regtools

• Matrix: Regtools/ursell_500
• Description: URSELL 500x500 Test problem: integral equation with no square integrable solution.
• download as a MATLAB mat-file, file size: 686 KB. Use SJget(259) or SJget('Regtools/ursell_500') 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 500 number of columns 500 structural full rank? yes structural rank 500 numerical rank 497 dimension of the numerical null space 3 numerical rank / min(size(A)) 0.994 Euclidean norm of A 0.53621 calculated singular value # 497 7.0579e-014 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 5.5511e-014 calculated singular value # 498 3.245e-014 gap in the singular values at the numerical rank: singular value # 497 / singular value # 498 2.175 calculated condition number 3.6412e+013 condest 1.5822e+014 nonzeros 250,000 # 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 259 UFid -

 Additional fields size and type b full 500-by-1

Notes:

```    Constructed by the call [A,b]= ursell(500)

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')) 125,250 125,250 Cholesky flop count 4.2e+007 4.2e+007 nnz(L+U), no partial pivoting 250,000 250,000 nnz(V) for QR, upper bound nnz(L) for LU 125,250 125,250 nnz(R) for QR, upper bound nnz(U) for LU 125,250 125,250

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.