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 | 200 |

structural full rank? | yes |

structural rank | 26 |

numerical rank | 25 |

dimension of the numerical null space | 175 |

numerical rank / min(size(A)) | 0.96154 |

Euclidean norm of A | 0.93258 |

calculated singular value # 25 | 3.2208e-014 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 2.2204e-014 |

calculated singular value # 26 | 1.9245e-015 |

gap in the singular values at the numerical rank: singular value # 25 / singular value # 26 | 16.736 |

calculated condition number | 4.8459e+014 |

condest | -2 |

nonzeros | 5,200 |

# 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 | 250 |

UFid | - |

Additional fields | size and type |

b | full 26-by-1 |

Notes:

Constructed by the call [A,b]= parallax(200) 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 | 4,875 | 4,875 |

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.