### Abstract

We present a new parallel algorithm for computing arbitrary functions of triangular matrices. The presented algorithm is the first one to date requiring polylogarithmic time, and computes an arbitrary function of an n×n triangular matrix in O(log^{3} n) time using O(n^{6}) processors. The algorithm requires the eigenvalues of the input matrix be distinct, and makes use of the commutativity relationship between the input and output matrices.

Original language | English (US) |
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Pages (from-to) | 85-92 |

Number of pages | 8 |

Journal | Computing (Vienna/New York) |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

Externally published | Yes |

### Keywords

- Divide and conquer
- Matrix functions
- Parlett's algorithm

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

Koç, Ç. K., & Bakkaloǧlu, B. (1996). A parallel algorithm for functions of triangular matrices.

*Computing (Vienna/New York)*,*57*(1), 85-92. https://doi.org/10.1007/BF02238360