### Abstract

Under-determined linear equation systems occur in different
engineering applications. In structural engineering they typically
appear when applying the force method. As an example one could
mention limit load analysis based on The Lower Bound Theorem. In
this application there is a set of under-determined equilibrium
equation restrictions in an LP-problem. A significant reduction of
computer time spent on solving the LP-problem is achieved if the
equilib rium equations are reduced before going into the
optimization procedure. Experience has shown that for some
structures one must apply full pivoting to ensure numerical
stability of the aforementioned reduction. Moreover the
coefficient matrix for the equilibrium equations is typically very
sparse. The objective is to deal efficiently with the full
pivoting reduction of sparse rectangular matrices using a dynamic
storage scheme based on the block matrix concept.

Original language | English |
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Title of host publication | Ninth Nordic Seminar on Computational Mechanics |

Place of Publication | Lyngby |

Publisher | BKM, DTU |

Publication date | 1996 |

Pages | 205-209 |

Publication status | Published - 1996 |

Event | 9th Nordic Seminar on Computational Mechanics - Lyngby, Denmark Duration: 25 Oct 1996 → 26 Oct 1996 Conference number: 9 |

### Conference

Conference | 9th Nordic Seminar on Computational Mechanics |
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Number | 9 |

Country | Denmark |

City | Lyngby |

Period | 25/10/1996 → 26/10/1996 |

## Cite this

Tarp-Johansen, N. J., Poulsen, P. N., & Damkilde, L. (1996). Reduction of Under-Determined Linear Systems by Sparce Block
Matrix Technique. In

*Ninth Nordic Seminar on Computational Mechanics*(pp. 205-209). BKM, DTU.