A note on Lanczos algorithm for computing pagerank

Kazuma Teramoto, Takashi Nodera

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationSpringer Proceedings in Mathematics and Statistics
PublisherSpringer New York LLC
Pages25-33
Number of pages9
Volume124
ISBN (Print)9783319161389
DOIs
Publication statusPublished - 2016
Event3rd Annual International Conference on Computational Mathematics, Computational Geometry and Statistics, CMCGS 2014 - Singapore, Singapore
Duration: 2014 Feb 32014 Feb 4

Other

Other3rd Annual International Conference on Computational Mathematics, Computational Geometry and Statistics, CMCGS 2014
CountrySingapore
CitySingapore
Period14/2/314/2/4

Fingerprint

Lanczos Algorithm
PageRank
Computing
Arnoldi Method
Nonsymmetric Matrix
Largest Eigenvalue
Tridiagonal matrix
Transform
Converge
Iteration
Numerical Results
Approximation

Keywords

  • Eigenvalue problem
  • Lanczos method
  • PageRank

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Teramoto, K., & Nodera, T. (2016). A note on Lanczos algorithm for computing pagerank. In 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.

Springer Proceedings in Mathematics and Statistics. Vol. 124 Springer New York LLC, 2016. p. 25-33.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Teramoto, K & Nodera, T 2016, A note on Lanczos algorithm for computing pagerank. in 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
Teramoto K, Nodera T. A note on Lanczos algorithm for computing pagerank. In Springer Proceedings in Mathematics and Statistics. Vol. 124. Springer New York LLC. 2016. p. 25-33 https://doi.org/10.5176/2251-1911_CMCGS14.15_3
Teramoto, Kazuma ; Nodera, Takashi. / A note on Lanczos algorithm for computing pagerank. Springer Proceedings in Mathematics and Statistics. Vol. 124 Springer New York LLC, 2016. pp. 25-33
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