### Abstract

A chained-matrices approach for parallel computing the nth convergent of continued fractions is presented. The resulting algorithm computes the entire prefix values of any continued fraction in O(log n) time on the EREW PRAM model or a network with O(n/log n) processors connected by the cube-connectedcycles, binary tree, perfect shuffle, or hypercube. It can be applied to approximate the transcendental numbers, such as π and e, in O(log m) time by using O(m/log m) processors for a result with m-digit precision. We also use it to costoptimally solve the second-order linear recurrence, the polynomial evaluation, the recurrence of vector norm, the general class of recurrence equation defined by Kogge and Stone (1973), and the general mth order linear recurrence. It is easy to implement because there are only some matrix multiplications and a division operation involved.

Original language | English |
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Pages (from-to) | 65-80 |

Number of pages | 16 |

Journal | Journal of Scientific Computing |

Volume | 9 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1994 Mar 1 |

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### Keywords

- Continued fractions
- parallel computation
- parallel-prefix problem
- polynomial evaluation
- recurrence equations

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Engineering(all)
- Computational Theory and Mathematics

### Cite this

**A chained-matrices approach for parallel computation of continued fractions and its applications.** / Lin, Shun-Shii.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A chained-matrices approach for parallel computation of continued fractions and its applications

AU - Lin, Shun-Shii

PY - 1994/3/1

Y1 - 1994/3/1

N2 - A chained-matrices approach for parallel computing the nth convergent of continued fractions is presented. The resulting algorithm computes the entire prefix values of any continued fraction in O(log n) time on the EREW PRAM model or a network with O(n/log n) processors connected by the cube-connectedcycles, binary tree, perfect shuffle, or hypercube. It can be applied to approximate the transcendental numbers, such as π and e, in O(log m) time by using O(m/log m) processors for a result with m-digit precision. We also use it to costoptimally solve the second-order linear recurrence, the polynomial evaluation, the recurrence of vector norm, the general class of recurrence equation defined by Kogge and Stone (1973), and the general mth order linear recurrence. It is easy to implement because there are only some matrix multiplications and a division operation involved.

AB - A chained-matrices approach for parallel computing the nth convergent of continued fractions is presented. The resulting algorithm computes the entire prefix values of any continued fraction in O(log n) time on the EREW PRAM model or a network with O(n/log n) processors connected by the cube-connectedcycles, binary tree, perfect shuffle, or hypercube. It can be applied to approximate the transcendental numbers, such as π and e, in O(log m) time by using O(m/log m) processors for a result with m-digit precision. We also use it to costoptimally solve the second-order linear recurrence, the polynomial evaluation, the recurrence of vector norm, the general class of recurrence equation defined by Kogge and Stone (1973), and the general mth order linear recurrence. It is easy to implement because there are only some matrix multiplications and a division operation involved.

KW - Continued fractions

KW - parallel computation

KW - parallel-prefix problem

KW - polynomial evaluation

KW - recurrence equations

UR - http://www.scopus.com/inward/record.url?scp=0028385358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028385358&partnerID=8YFLogxK

U2 - 10.1007/BF01573178

DO - 10.1007/BF01573178

M3 - Article

AN - SCOPUS:0028385358

VL - 9

SP - 65

EP - 80

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 1

ER -