• SJSU Singular Matrix Database
• Matrix group: Regtools

• Matrix: Regtools/baart_500
• Description: BAART 500x500 Test problem: Fredholm integral equation of the first kind.
• download as a MATLAB mat-file, file size: 2 MB. Use SJget(235) or SJget('Regtools/baart_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 12 dimension of the numerical null space 488 numerical rank / min(size(A)) 0.024 Euclidean norm of A 3.2287 calculated singular value # 12 3.0107e-013 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 2.2204e-013 calculated singular value # 13 2.0864e-013 gap in the singular values at the numerical rank: singular value # 12 / singular value # 13 1.443 calculated condition number 1.1602e+018 condest 1.4374e+019 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 0% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author Baart editor Per Christian Hansen date 1982 kind ill-posed problem 2D/3D problem? no SJid 235 UFid -

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

Notes:

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

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

[A,b,x] = baart(n)

Discretization of a first-kind Fredholm integral equation with
kernel K and right-hand side g given by
K(s,t) = exp(s*cos(t)) ,  g(s) = 2*sinh(s)/s ,
and with integration intervals  sin [0,pi/2] ,  t in [0,pi] .
The solution is given by
f(t) = sin(t) .

The order n must be even.
```

 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.