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 64799 to 64804 and associated error bounds.

Matrix properties (click for a legend) | |

number of rows | 64,810 |

number of columns | 64,810 |

structural full rank? | yes |

structural rank | 64,810 |

numerical rank | 64,801 |

dimension of the numerical null space | 9 |

numerical rank / min(size(A)) | 0.99986 |

Euclidean norm of A | 4.1067e+008 |

calculated singular value # 64801 | 0.0039293 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 0.003863 |

calculated singular value # 64802 | 0.0036578 |

gap in the singular values at the numerical rank: singular value # 64801 / singular value # 64802 | 1.0742 |

calculated condition number | -2 |

condest | 5.3237e+012 |

nonzeros | 565,996 |

# of blocks from dmperm | 6 |

# strongly connected comp. | 6 |

entries not in dmperm blocks | 15 |

explicit zero entries | 10 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | IBM |

editor | O. Schenk |

date | 2004 |

kind | optimization problem |

2D/3D problem? | no |

SJid | 514 |

UFid | 1,225 |

Additional fields | size and type |

b | full 64810-by-1 |

Notes:

Revised Nov 2006; relative eps changes to A, right-hand-side added. Note that this matrix should have been placed in the Schenk_IBMNA/ directory when it was first added in August 2004, but moving it now would disrupt exising users of the collection.

Ordering statistics: | AMD |
METIS |
DMPERM+ |

nnz(chol(P*(A+A'+s*I)*P')) | 6,523,400 | 5,247,637 | 5,522,952 |

Cholesky flop count | 1.2e+010 | 5.1e+009 | 5.7e+009 |

nnz(L+U), no partial pivoting | 12,981,990 | 10,430,464 | 10,981,109 |

nnz(V) for QR, upper bound nnz(L) for LU | 70,689,995 | 34,052,057 | 33,801,713 |

nnz(R) for QR, upper bound nnz(U) for LU | 115,405,123 | 70,190,882 | 69,487,093 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 10 explicit zero entries.
*

*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.
*