• SJSU Singular Matrix Database
• Matrix group: Regtools

• Matrix: Regtools/wing_200
• Description: WING 200x200 Test problem with a discontinuous solution.
• download as a MATLAB mat-file, file size: 286 KB. Use SJget(262) or SJget('Regtools/wing_200') 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 200 number of columns 200 structural full rank? yes structural rank 200 numerical rank 8 dimension of the numerical null space 192 numerical rank / min(size(A)) 0.04 Euclidean norm of A 0.44698 calculated singular value # 8 4.3861e-013 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 1.1102e-014 calculated singular value # 9 3.4287e-015 gap in the singular values at the numerical rank: singular value # 8 / singular value # 9 127.93 calculated condition number 9.0353e+019 condest 2.5503e+020 nonzeros 40,000 # 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 0% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author Wing and Zahrt editor Per Christian Hansen date 1991 kind ill-posed problem 2D/3D problem? no SJid 262 UFid -

 Additional fields size and type b full 200-by-1 x full 200-by-1

Notes:

```    Constructed by the call [A,b,x]= wing(200)

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

[A,b,x] = wing(n,t1,t2)

Discretization of a first kind Fredholm integral eqaution with
kernel K and right-hand side g given by
K(s,t) = t*exp(-s*t^2)                       0 < s,t < 1
g(s)   = (exp(-s*t1^2) - exp(-s*t2^2)/(2*s)  0 < s   < 1
and with the solution f given by
f(t) = | 1  for  t1 < t < t2
| 0  elsewhere.

Here, t1 and t2 are constants satisfying t1 < t2.  If they are
not speficied, the values t1 = 1/3 and t2 = 2/3 are used.
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 20,100 20,100 Cholesky flop count 2.7e+006 2.7e+006 nnz(L+U), no partial pivoting 40,000 40,000 nnz(V) for QR, upper bound nnz(L) for LU 20,100 20,100 nnz(R) for QR, upper bound nnz(U) for LU 20,100 20,100

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.