HENRICI, P.: On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices. J. Soc. Ind. Appl. Math. 6, 144-162 (1958).

Crossref

Google Scholar

[4]

JACOBI, C. G. J.: Über ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen. Crelle's Journal 30, 51-94 (1846).

Crossref

Google Scholar

[5]

POPE, D. A., and C. TOMPKINS: Maximizing functions of rotations-experiments concerning speed of diagonalisation of symmetric matrices using Jacobi's method. J. Ass. Comp. Mach. 4, 459-466 (1957).

Digital Library

Google Scholar

[6]

RUTISHAUSER, H., and H. R. SCHWARZ: The LR-transformation method for symmetric matrices. Numer. Math. 5, 273-289 (1963).

Digital Library

Google Scholar

[7]

SCHOENHAGE, A.: Zur Konvergenz des Jacobi-Verfahrens. Num. Math. 3, 374- 380 (1961).

Digital Library

Google Scholar

[8]

WILKINSON, J. H.: Note on the quadratic convergence of the cyclic Jacobi process. Numer. Math. 4, 296-300 (1962).

Digital Library

Google Scholar

[9]

WILKINSON, J. H.: Householder's method for symmetric matrices. Numer. Math. 4, 354-361 (1962).

Digital Library

Google Scholar

[10]

WILKINSON, J. H.: Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection. Numer. Math. 4, 362-367 (1962).

Digital Library

Google Scholar

[11]

WILKINSON, J. H.: Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration. Numer. Math. 4, 368-372 (1962).

Digital Library

Google Scholar

[12]

WILKINSON, J. H.: The algebraic eigenvalue problem, 662 p. Oxford: Clarendon Press 1965.

Crossref

Google Scholar

Cited By

View all

Chiyonobu MMiyamae TTakata MHarayama JKimura KNakamura Y(2024)Singular value decomposition for complex matrices using two-sided Jacobi methodThe Journal of Supercomputing10.1007/s11227-024-05903-680:8(11719-11740)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s11227-024-05903-6
Zhao HCheng ZHan CGuo HSun L(2024)A novel memristor-based method to compute eigenpairsAnalog Integrated Circuits and Signal Processing10.1007/s10470-023-02214-3118:1(109-119)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s10470-023-02214-3
Murakami H(2021)Single-Precision Calculation of Iterative Refinement of Eigenpairs of a Real Symmetric-Definite Generalized Eigenproblem by Using a Filter Composed of a Single ResolventThe International Conference on High Performance Computing in Asia-Pacific Region Companion10.1145/3440722.3440784(11-20)Online publication date: 20-Jan-2021
https://dl.acm.org/doi/10.1145/3440722.3440784
Show More Cited By

Recommendations

Accuracy of the Jacobi Method on Scaled Diagonally Dominant Symmetric Matrices

This paper proves that the two-sided Jacobi method computes the eigenvalues of the indefinite symmetric matrix to high relative accuracy, provided that the initial matrix is scaled diagonally dominant. It proves sharp eigenvalue perturbation bounds ...
Constraint Preconditioners for Symmetric Indefinite Matrices

We study the eigenvalue bounds of block two-by-two nonsingular and symmetric indefinite matrices whose $(1,1)$ block is symmetric positive definite and Schur complement with respect to its $(2,2)$ block is symmetric indefinite. A constraint ...
High performance parallel approximate eigensolver for real symmetric matrices

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Numerische Mathematik Volume 9, Issue 1

November 1966

102 pages

ISSN:0029-599X

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 November 1966

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 25 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Chiyonobu MMiyamae TTakata MHarayama JKimura KNakamura Y(2024)Singular value decomposition for complex matrices using two-sided Jacobi methodThe Journal of Supercomputing10.1007/s11227-024-05903-680:8(11719-11740)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s11227-024-05903-6
Zhao HCheng ZHan CGuo HSun L(2024)A novel memristor-based method to compute eigenpairsAnalog Integrated Circuits and Signal Processing10.1007/s10470-023-02214-3118:1(109-119)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s10470-023-02214-3
Murakami H(2021)Single-Precision Calculation of Iterative Refinement of Eigenpairs of a Real Symmetric-Definite Generalized Eigenproblem by Using a Filter Composed of a Single ResolventThe International Conference on High Performance Computing in Asia-Pacific Region Companion10.1145/3440722.3440784(11-20)Online publication date: 20-Jan-2021
https://dl.acm.org/doi/10.1145/3440722.3440784
Muthukrishnan HNellans DLustig DFessler JWenisch TMartínez JDuato JJohn L(2021)Efficient multi-GPU shared memory via automatic optimization of fine-grained transfersProceedings of the 48th Annual International Symposium on Computer Architecture10.1109/ISCA52012.2021.00020(139-152)Online publication date: 14-Jun-2021
https://dl.acm.org/doi/10.1109/ISCA52012.2021.00020
Albataineh ZSalem F(2021)Two pairwise iterative schemes for high dimensional blind source separationInternational Journal of Speech Technology10.1007/s10772-020-09729-424:4(957-968)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s10772-020-09729-4
Albataineh Z(2018)Blind Decoding of Massive MIMO Uplink Systems Based on the Higher Order CumulantsWireless Personal Communications: An International Journal10.1007/s11277-018-5883-2103:2(1835-1847)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s11277-018-5883-2
Hari V(2018)Globally convergent Jacobi methods for positive definite matrix pairsNumerical Algorithms10.1007/s11075-017-0435-579:1(221-249)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s11075-017-0435-5
Cheng SCai ZLi JGao H(2017)Extracting Kernel Dataset from Big Sensory Data in Wireless Sensor NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2016.264521229:4(813-827)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1109/TKDE.2016.2645212
Albataineh ZSalem F(2015)Robust Blind Multiuser Detection Algorithm Using Fourth-Order Cumulant MatricesCircuits, Systems, and Signal Processing10.1007/s00034-014-9944-934:8(2577-2595)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1007/s00034-014-9944-9
Venanzi MRogers AJennings NGini MShehory OIto TJonker C(2013)Trust-based fusion of untrustworthy information in crowdsourcing applicationsProceedings of the 2013 international conference on Autonomous agents and multi-agent systems10.5555/2484920.2485052(829-836)Online publication date: 6-May-2013
https://dl.acm.org/doi/10.5555/2484920.2485052
Show More Cited By

Abstract

References

Cited By

Recommendations

Accuracy of the Jacobi Method on Scaled Diagonally Dominant Symmetric Matrices

Constraint Preconditioners for Symmetric Indefinite Matrices

High performance parallel approximate eigensolver for real symmetric matrices

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Share

Share this Publication link

Share on social media

Affiliations