• SJSU Singular Matrix Database
• Matrix group: Regtools
• Click here for a description of the Regtools group.
• Click here for a list of all matrices
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• Matrix: Regtools/i_laplace_500
• Description: I_LAPLACE 500x500 Test problem: inverse Laplace transformation.
• download as a MATLAB mat-file, file size: 829 KB. Use SJget(247) or SJget('Regtools/i_laplace_500') in MATLAB.
• download in Matrix Market format, file size: 1 MB.
• download in Rutherford/Boeing format, file size: 1 MB.

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? no structural rank 363 numerical rank 39 dimension of the numerical null space 461 numerical rank / min(size(A)) 0.078 Euclidean norm of A 5.3209 calculated singular value # 39 7.505e-013 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 4.4409e-013 calculated singular value # 40 2.9763e-013 gap in the singular values at the numerical rank: singular value # 39 / singular value # 40 2.5216 calculated condition number Inf condest Inf nonzeros 104,149 # of blocks from dmperm 16 # strongly connected comp. 31 explicit zero entries 0 nonzero pattern symmetry 76% numeric value symmetry 0% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author Varah editor Per Christian Hansen date 1983 kind ill-posed problem 2D/3D problem? no SJid 247 UFid -

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

Notes:

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

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

[A,b,x,t] = i_laplace(n,example)

Discretization of the inverse Laplace transformation by means of
Gauss-Laguerre quadrature.  The kernel K is given by
K(s,t) = exp(-s*t) ,
and both integration intervals are [0,inf).

The following examples are implemented, where f denotes
the solution, and g denotes the right-hand side:
1: f(t) = exp(-t/2),        g(s) = 1/(s + 0.5)
2: f(t) = 1 - exp(-t/2),    g(s) = 1/s - 1/(s + 0.5)
3: f(t) = t^2*exp(-t/2),    g(s) = 2/(s + 0.5)^3
4: f(t) = | 0 , t <= 2,     g(s) = exp(-2*s)/s.
| 1 , t >  2

The quadrature points are returned in the vector t.
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 65,501 65,034 Cholesky flop count 9.7e+006 9.5e+006 nnz(L+U), no partial pivoting 130,502 129,568 nnz(V) for QR, upper bound nnz(L) for LU 58,878 124,815 nnz(R) for QR, upper bound nnz(U) for LU 110,715 110,715

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.