Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

Matrix properties (click for a legend) | |

number of rows | 1,000 |

number of columns | 1,000 |

structural full rank? | yes |

structural rank | 1,000 |

numerical rank | 13 |

dimension of the numerical null space | 987 |

numerical rank / min(size(A)) | 0.013 |

Euclidean norm of A | 3.2287 |

calculated singular value # 13 | 6.2579e-013 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 4.4409e-013 |

calculated singular value # 14 | 3.7232e-013 |

gap in the singular values at the numerical rank: singular value # 13 / singular value # 14 | 1.6808 |

calculated condition number | 2.7584e+018 |

condest | 7.7812e+020 |

nonzeros | 1,000,000 |

# 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 | 236 |

UFid | - |

Additional fields | size and type |

b | full 1000-by-1 |

x | full 1000-by-1 |

Notes:

Constructed by the call [A,b,x]= baart(1000) 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')) | 500,500 | 500,500 |

Cholesky flop count | 3.3e+008 | 3.3e+008 |

nnz(L+U), no partial pivoting | 1,000,000 | 1,000,000 |

nnz(V) for QR, upper bound nnz(L) for LU | 500,500 | 500,500 |

nnz(R) for QR, upper bound nnz(U) for LU | 500,500 | 500,500 |

*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.