**Matrix: Koutsovasilis/F2**

Description: AUDI engine piston rod; Panos Koutsovasilis, Technische Univ. Dresden

(undirected graph drawing) |

Matrix properties | |

number of rows | 71,505 |

number of columns | 71,505 |

nonzeros | 5,294,285 |

structural full rank? | yes |

structural rank | 71,505 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | yes |

positive definite? | no |

author | P. Koutsovasilis |

editor | T. Davis |

date | 2007 |

kind | structural problem |

2D/3D problem? | yes |

Notes:

Stiffness matrix from an AUDI engine piston rod. This matrix is an ill- condition symmetric indefinite matrix. In MATLAB 7.4, the matrix is factorized three times in x=A\b. Inside backslash, CHOLMOD is tried first since the matrix is symmetric and all diagonal entries are positive. CHOLMOD fails since the matrix is indefinite. Next, UMFPACK is used with default pivot tolerances which maintain sparsity at the (rare) expense of a slight decrease in accuracy. This succeeds, but the result is flagged as potentially inaccurate because the condition estimate is high. UMFPACK is then used again with more conservative tolerances (but more fill-in).

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 20,756,208 |

Cholesky flop count | 1.2e+10 |

nnz(L+U), no partial pivoting, with AMD | 41,440,911 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 40,210,857 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 109,796,898 |

For a description of the statistics displayed above, click here.

*Maintained by Tim Davis, last updated 12-Mar-2014.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
*