### 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) |
---|---|

Pages (from-to) | 85-92 |

Number of pages | 8 |

Journal | Computing (Vienna/New York) |

Volume | 57 |

Issue number | 1 |

State | Published - 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Theoretical Computer Science

### Cite this

*Computing (Vienna/New York)*,

*57*(1), 85-92.

**A parallel algorithm for functions of triangular matrices.** / Koç, Ç K.; Bakkaloglu, Bertan.

Research output: Contribution to journal › Article

*Computing (Vienna/New York)*, vol. 57, no. 1, pp. 85-92.

}

TY - JOUR

T1 - A parallel algorithm for functions of triangular matrices

AU - Koç, Ç K.

AU - Bakkaloglu, Bertan

PY - 1996

Y1 - 1996

N2 - 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(log3 n) time using O(n6) 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.

AB - 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(log3 n) time using O(n6) 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.

KW - Divide and conquer

KW - Matrix functions

KW - Parlett's algorithm

UR - http://www.scopus.com/inward/record.url?scp=0029695377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029695377&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029695377

VL - 57

SP - 85

EP - 92

JO - Computing

JF - Computing

SN - 0010-485X

IS - 1

ER -