• SJSU Singular Matrix Database
• Matrix group: Regtools

• Matrix: Regtools/i_laplace_100
• Description: I_LAPLACE 100x100 Test problem: inverse Laplace transformation.
• download as a MATLAB mat-file, file size: 63 KB. Use SJget(245) or SJget('Regtools/i_laplace_100') 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 100 number of columns 100 structural full rank? yes structural rank 100 numerical rank 28 dimension of the numerical null space 72 numerical rank / min(size(A)) 0.28 Euclidean norm of A 2.3749 calculated singular value # 28 9.0882e-014 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 4.4409e-014 calculated singular value # 29 1.2597e-014 gap in the singular values at the numerical rank: singular value # 28 / singular value # 29 7.2149 calculated condition number 5.5101e+032 condest 9.9509e+049 nonzeros 7,590 # of blocks from dmperm 1 # strongly connected comp. 1 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry 91% 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 245 UFid -

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

Notes:

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

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')) 5,004 5,050 Cholesky flop count 3.3e+005 3.4e+005 nnz(L+U), no partial pivoting 9,908 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.