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

Matrix properties (click for a legend) | |

number of rows | 4,101 |

number of columns | 4,101 |

structural full rank? | yes |

structural rank | 4,101 |

numerical rank | 4,099 |

dimension of the numerical null space | 2 |

numerical rank / min(size(A)) | 0.99951 |

Euclidean norm of A | 2.0176e+006 |

calculated singular value # 4099 | 1.0001e-005 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 9.5484e-007 |

calculated singular value # 4100 | 6.8627e-011 |

gap in the singular values at the numerical rank: singular value # 4099 / singular value # 4100 | 1.4573e+005 |

calculated condition number | 7.0298e+017 |

condest | 6.7122e+020 |

nonzeros | 36,879 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

entries not in dmperm blocks | 0 |

explicit zero entries | 0 |

nonzero pattern symmetry | 50% |

numeric value symmetry | 0% |

type | real |

structure | unsymmetric |

Cholesky candidate? | no |

positive definite? | no |

author | B. Muite |

editor | T. Davis |

date | 2007 |

kind | structural problem |

2D/3D problem? | yes |

SJid | 332 |

UFid | 1,866 |

Notes:

Chebyshev integration matrix from Benson Muite, Oxford. Details of the matrices can be found in a preprint at http://www.maths.ox.ac.uk/~muite entitled "A comparison of Chebyshev methods for solving fourth-order semilinear initial boundary value problems," June 2007. These matrices are very ill-conditioned, partly because of the dense rows which are hard to scale when coupled with the rest of the matrix.

Ordering statistics: | AMD |
METIS |

nnz(chol(P*(A+A'+s*I)*P')) | 28,683 | 37,804 |

Cholesky flop count | 2.0e+005 | 3.5e+005 |

nnz(L+U), no partial pivoting | 53,265 | 71,507 |

nnz(V) for QR, upper bound nnz(L) for LU | 20,493 | 20,493 |

nnz(R) for QR, upper bound nnz(U) for LU | 8,411,151 | 8,411,151 |

*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.