### Abstract

We present a polynomial-time algorithm to improve the performance of computing the Hessian of a vector-valued function. The values of the Hessian derivatives are calculated by applying face, edge, or vertex elimination operations on a symmetric computational graph. Our algorithm detects symmetry in the graph by matching the vertices and edges with their corresponding pairs; thereby enabling us to identify duplicate operations. Through the detection of symmetry, the computation costs can potentially be halved by performing only one of each of these operations.

Original language | English (US) |
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Title of host publication | Advances in Automatic Differentiation |

Pages | 91-102 |

Number of pages | 12 |

DOIs | |

State | Published - 2008 |

Event | 5th International Conference on Automatic Differentiation - Bonn, Germany Duration: Aug 11 2008 → Aug 15 2008 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 64 LNCSE |

ISSN (Print) | 1439-7358 |

### Conference

Conference | 5th International Conference on Automatic Differentiation |
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Country | Germany |

City | Bonn |

Period | 8/11/08 → 8/15/08 |

### Keywords

- Directed acyclic graph
- Hessian computational graphs
- Symmetry

### ASJC Scopus subject areas

- Modeling and Simulation
- Engineering(all)
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Mathematics

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## Cite this

Bhowmick, S., & Hovland, P. D. (2008). A polynomial-time algorithm for detecting directed axial symmetry in Hessian computational graphs. In

*Advances in Automatic Differentiation*(pp. 91-102). (Lecture Notes in Computational Science and Engineering; Vol. 64 LNCSE). https://doi.org/10.1007/978-3-540-68942-3_9