A singular value of A is guaranteed^{1} to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.

Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 11442 to 11445 and associated error bounds.

Matrix properties (click for a legend) | |

number of rows | 11,445 |

number of columns | 11,445 |

structural full rank? | yes |

structural rank | 11,445 |

numerical rank | 11,444 |

dimension of the numerical null space | 1 |

numerical rank / min(size(A)) | 0.99991 |

Euclidean norm of A | 266.27 |

calculated singular value # 11444 | 1.6337e-007 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 6.5057e-010 |

calculated singular value # 11445 | 1.9906e-014 |

gap in the singular values at the numerical rank: singular value # 11444 / singular value # 11445 | 8.2071e+006 |

calculated condition number | 1.3376e+016 |

condest | 1.2623e+017 |

nonzeros | 176,117 |

# 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 | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | E. Rudnyi |

editor | E. Rudnyi |

date | 2004 |

kind | model reduction problem |

2D/3D problem? | yes |

SJid | 399 |

UFid | 1,204 |

Additional fields | size and type |

E | sparse 11445-by-11445 |

B | sparse 11445-by-1 |

C | sparse 7-by-11445 |

cname | full 7-by-7 |

Notes:

Primary matrix in this model reduction problem is the Oberwolfach A matrix

Ordering statistics: | AMD |
METIS |

nnz(chol(P*(A+A'+s*I)*P')) | 491,255 | 483,544 |

Cholesky flop count | 4.1e+007 | 3.3e+007 |

nnz(L+U), no partial pivoting | 971,065 | 955,643 |

nnz(V) for QR, upper bound nnz(L) for LU | 841,710 | 826,206 |

nnz(R) for QR, upper bound nnz(U) for LU | 2,001,083 | 1,879,892 |

*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.