### Abstract

We now study the Lanczos algorithm for computing the PageRank vector. This algorithm is based on biorthogonalization, which transforms a nonsymmetric matrix into a tridiagonal matrix to compute PageRank. This generates better approximation of the largest eigenvalue at early stage of iterations. We propose a practical scheme of the Lanczos biorthogonalization algorithm with SVD scheme for computing PageRank. Numerical results show that the proposed algorithm converges faster than the existing Arnoldi method in the computation time.

Original language | English |
---|---|

Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 25-33 |

Number of pages | 9 |

Volume | 124 |

ISBN (Print) | 9783319161389 |

DOIs | |

Publication status | Published - 2016 |

Event | 3rd Annual International Conference on Computational Mathematics, Computational Geometry and Statistics, CMCGS 2014 - Singapore, Singapore Duration: 2014 Feb 3 → 2014 Feb 4 |

### Other

Other | 3rd Annual International Conference on Computational Mathematics, Computational Geometry and Statistics, CMCGS 2014 |
---|---|

Country | Singapore |

City | Singapore |

Period | 14/2/3 → 14/2/4 |

### Fingerprint

### Keywords

- Eigenvalue problem
- Lanczos method
- PageRank

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Springer Proceedings in Mathematics and Statistics*(Vol. 124, pp. 25-33). Springer New York LLC. https://doi.org/10.5176/2251-1911_CMCGS14.15_3

**A note on Lanczos algorithm for computing pagerank.** / Teramoto, Kazuma; Nodera, Takashi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Springer Proceedings in Mathematics and Statistics.*vol. 124, Springer New York LLC, pp. 25-33, 3rd Annual International Conference on Computational Mathematics, Computational Geometry and Statistics, CMCGS 2014, Singapore, Singapore, 14/2/3. https://doi.org/10.5176/2251-1911_CMCGS14.15_3

}

TY - GEN

T1 - A note on Lanczos algorithm for computing pagerank

AU - Teramoto, Kazuma

AU - Nodera, Takashi

PY - 2016

Y1 - 2016

N2 - We now study the Lanczos algorithm for computing the PageRank vector. This algorithm is based on biorthogonalization, which transforms a nonsymmetric matrix into a tridiagonal matrix to compute PageRank. This generates better approximation of the largest eigenvalue at early stage of iterations. We propose a practical scheme of the Lanczos biorthogonalization algorithm with SVD scheme for computing PageRank. Numerical results show that the proposed algorithm converges faster than the existing Arnoldi method in the computation time.

AB - We now study the Lanczos algorithm for computing the PageRank vector. This algorithm is based on biorthogonalization, which transforms a nonsymmetric matrix into a tridiagonal matrix to compute PageRank. This generates better approximation of the largest eigenvalue at early stage of iterations. We propose a practical scheme of the Lanczos biorthogonalization algorithm with SVD scheme for computing PageRank. Numerical results show that the proposed algorithm converges faster than the existing Arnoldi method in the computation time.

KW - Eigenvalue problem

KW - Lanczos method

KW - PageRank

UR - http://www.scopus.com/inward/record.url?scp=84955322856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955322856&partnerID=8YFLogxK

U2 - 10.5176/2251-1911_CMCGS14.15_3

DO - 10.5176/2251-1911_CMCGS14.15_3

M3 - Conference contribution

AN - SCOPUS:84955322856

SN - 9783319161389

VL - 124

SP - 25

EP - 33

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -