• SJSU Singular Matrix Database
• Matrix group: Regtools

• Matrix: Regtools/parallax_1000
• Description: PARALLAX 26x1000 Stellar parallax problem with 28 fixed, real observations.
• download as a MATLAB mat-file, file size: 172 KB. Use SJget(252) or SJget('Regtools/parallax_1000') 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 26 number of columns 1,000 structural full rank? yes structural rank 26 numerical rank 24 dimension of the numerical null space 976 numerical rank / min(size(A)) 0.92308 Euclidean norm of A 0.93258 calculated singular value # 24 3.8521e-013 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 1.1102e-013 calculated singular value # 25 3.336e-014 gap in the singular values at the numerical rank: singular value # 24 / singular value # 25 11.547 calculated condition number 4.6294e+014 condest -2 nonzeros 26,000 # of blocks from dmperm 1 # strongly connected comp. 1 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry 0% numeric value symmetry 0% type real structure rectangular Cholesky candidate? no positive definite? no

 author Smart editor Per Christian Hansen date 1938 kind ill-posed problem 2D/3D problem? no SJid 252 UFid -

 Additional fields size and type b full 26-by-1

Notes:

```    Constructed by the call [A,b]= parallax(1000)

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

[A,b] = parallax(n)

Stellar parallax problem with 28 fixed, real observations.

The underlying problem is a Fredholm integral equation of the
first kind with kernel
K(s,t) = (1/sigma*sqrt(2*pi))*exp(-0.5*((s-t)/sigma)^2) ,
and it is discretized by means of a Galerkin method with n
orthonormal basis functions.  The right-hand side consists of
a measured distribution function of stellar parallaxes, and its
length is fixed, m = 26.  The exact solution, which represents
the true distribution of stellar parallaxes, in not known.
```

 Ordering statistics: AMD METIS nnz(V) for QR, upper bound nnz(L) for LU 25,675 25,675 nnz(R) for QR, upper bound nnz(U) for LU 351 351

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.