Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Julia and Singularity for High Performance Computing Read chapter Read first chapter

2021 | OriginalPaper | Chapter

On an Implementation of the One-Sided Jacobi Method with High Accuracy

Authors : Masami Takata, Sho Araki, Kinji Kimura, Yoshimasa Nakamura

Published in: Advances in Parallel & Distributed Processing, and Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The one-sided Jacobi method for performing singular value decomposition can compute all singular values and singular vectors with high accuracy. Additionally, the computation cost is insignificant for comparatively small matrices. However, in the case of the conventional implementation in Linear Algebra PACKage, the subroutine may not be able to compute a singular vector with sufficient orthogonality. To avoid this problem, we propose a novel implementation of the one-sided Jacobi method. In the proposed implementation, a Givens rotation with high accuracy and fused multiply-accumulate are adopted.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Application of the Orthogonal QD Algorithm with Shift to Singular Value Decomposition for Large Sparse Matrices
next chapter Improvement of Island Genetic Algorithm Using Multiple Fitness Functions
Literature
1.
S. Araki, H. Tanaka, M. Takata, K. Kimura, Y. Nakamura, Fast computation method of column space by using the DQDS method and the OQDS method, in Proceedings of PDPTA 2018 (2018), pp. 333–339
2.
R.P. Brent, F.T. Luk, C. van Loan, Computation of the singular value decomposition using mesh-connected processors. J. VLSI Comput. Syst. 1, 242–270 (1985)MathSciNetMATH
3.
4.
J. Demmel, K. Veselic, Jacobi’s method is more accurate than QR. SIAM J. Matrix Anal. Appl. 13(4), 1204–1245 (1992)MathSciNetCrossRef
5.
J. Drmac, K. Veselic, New fast and accurate Jacobi SVD algorithm: I. SIAM J. Matrix Anal. Appl. 29, 1322–1342 (2008)MathSciNetCrossRef
6.
Z. Drmac, K. Veselic, New fast and accurate Jacobi SVD algorithm: II.. SIAM J. Matrix Anal. Appl. 29, 1343–1362 (2008)MathSciNetCrossRef
7.
K.V. Fernando, B.N. Parlett, Accurate singular values and differential qd algorithms. Numer. Math. 67, 191–229 (1994)MathSciNetCrossRef
8.
G.E. Forsythe, P. Henrici, The cyclic Jacobi method for computing the principal values of a complex matrix. Trans. Am. Math. Soc. 94, 1–23 (1960)MathSciNetCrossRef
9.
E. Kogbetliantz, Solution of linear equations by diagonalization of coefficients matrix. Q. Appl. Math. 13, 123–132 (1955)MathSciNetCrossRef
10.
11.
12.
B.N. Parlett, O.A. Marques, An implementation of the dqds algorithm (positive case). Lin. Alg. Appl 309(1–3), 217–259 (2000)MathSciNetCrossRef
13.
P.P.M. De Rijk, A one-sided Jacobi algorithm for computing the singular value decomposition on a vector computer. SIAM J. Sci. Stat. Comput. 10, 359–371 (1998)MathSciNetCrossRef
14.
15.
T. Sakurai, H. Tadano, CIRR: A Rayleigh-Ritz type method with counter integral for generalized eigenvalue problems. Hokkaido Math. J. 36, 745–757 (2007)MathSciNetCrossRef
Metadata
Title
On an Implementation of the One-Sided Jacobi Method with High Accuracy
Authors
Masami Takata
Sho Araki
Kinji Kimura
Yoshimasa Nakamura
Copyright Year
2021
Book
Advances in Parallel & Distributed Processing, and Applications

Print ISBN: 978-3-030-69983-3

Electronic ISBN: 978-3-030-69984-0

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-69984-0_51