@inproceedings{ls_leimeister, address = {Geetbets, Belgium (accepted for publication)}, author = {Peters, C.}, booktitle = {21st European Conference on Information Systems Doctoral Consortium (ECIS 2013 DC)}, interhash = {a4f5ccf63f0d61cf685209704f45fb30}, intrahash = {94a3b1575f454573aa2944c3086de0aa}, note = {JML_398}, title = {A Modularization Method for Telemedical Services}, year = 2013 } @inproceedings{ls_leimeister, address = {Utrecht, Netherlands (accepted for publication)}, author = {Peters, C. and Leimeister, J. M.}, booktitle = {21st European Conference on Information Systems (ECIS)}, interhash = {f881ff86349dbe8d652e8ec1ec6a8959}, intrahash = {e3b48e6271b654215252859d4839f964}, note = {JML_407}, title = {TM³ - A Modularization Method for Telemedical Services: Design and Evaluation}, year = 2013 } @inproceedings{ls_leimeister, address = {Hamburg, Germany}, author = {Peters, C. and Leimeister, J. M.}, booktitle = {4th International Service Modularity Seminar }, interhash = {3e55a560fc9e87e9ec82557c457b06c1}, intrahash = {8d4ceecb6718532f4c341fd8d93ef8a0}, note = {JML_392}, title = {The Design and Evaluation of TM³ - A Modularization Method for Telemedical Services}, year = 2013 } @book{Shawe:2004, address = {Cambridge, UK}, author = {Shawe-Taylor, John and Cristianini, Nello}, interhash = {ba08fe16ecfaaef17b41d9e432a4341e}, intrahash = {1d17b9d54a4ef23864227f647622d071}, publisher = {Cambridge University Press}, title = {Kernel Methods for Pattern Analysis}, year = 2004 } @article{355946, abstract = { A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
ACM Portal HeBIS: Universitaetsbibliothek Kassel
  Subscribe (Full Service)    Register (Limited Service, Free)    Login
  Search:   The ACM Digital Library   The Guide
  
ACM Home Page
Please provide us with feedback. Feedback
A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
Full text PdfPdf (977 KB)
Source ACM Transactions on Mathematical Software (TOMS) archive
Volume 7 ,  Issue 2  (June 1981) table of contents
Pages: 149 - 169  
Year of Publication: 1981
ISSN:0098-3500
Authors
Gene H. Golub  Department of Computer Science, Cornell University, Ithaca, NY
Franklin T. Luk  Department of Computer Science, Cornell University, Ithaca, NY
Michael L. Overton  Courant Institute of Mathematical Sciences, New York University, New York
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 11,   Downloads (12 Months): 80,   Citation Count: 2
Additional Information:

references   cited by   index terms   collaborative colleagues   peer to peer  

Tools and Actions: Request Permissions Request Permissions    Review this Article  
DOI Bookmark: Use this link to bookmark this Article: http://doi.acm.org/10.1145/355945.355946
What is a DOI?

REFERENCES
 
1
CULLUM, J. The simultaneous computation of a few algebraically largest and smallest elgenvalues of a large, sparse, symmetric matrix. Rep. RC 6827, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1977.
 
2
CULLUM, J., AND DONATH, W.E. A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matmces. In Proc. 1974 IEEE Conf on Decas~on and Control, Phoenix, Ariz., 1974, pp. 505-509.
 
3
CULLUM, J., AND WILLOUGHBY, R.A. Computing singular values and corresponding singular vectors of large matrices by Lanczos tridiagonalization. Rep. RC 8200, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1980.
 
4
GENTLEMAN, W.M. Least squares computations by Givens transformations w~thout square roots. JIMA 12 (1973), 329-336.
 
5
GOLUB, G H, AND KAHAN, W Calculating the singular values and pseudo-inverse of a matrix. SIAM J. Numer Anal. 2 (1965), 205-224.
 
6
GOLUB, G.H., AND LUK, F T. Singular value decomposition: Apphcations and computations. ARO Rep. 77-1, in Trans. 22nd Conf. of Army Mathematw~ans, 1977, pp. 577-605.
 
7
Gene H. Golub , Franklin T. Luk , Michael L. Overton, A block Lanczos method to compute the singular values and corresponding singular vectors of a matrix, Stanford University, Stanford, CA, 1977
 
8
GOLUB, G.H., AND REINSCH, C Singular value decomposition and least squares solutions. Numer. Math. 14 (1970), 403-420.
 
9
GOLUB, G H., AND UNDERWOOD, R. The block Lanczos method for computing elgenvalues. In Mathematical Software III, J.R. Rice (Ed.), Academic Press, New York, 1977, pp. 361-377.
 
10
LANCZOS, C L~near D~fferential Operators Van Nostrand, London, 1961.
 
11
John Gregg Lewis, Algorithms for sparse matrix eigenvalue problems., 1977
 
12
ORTEGA, J.M. Numerical Analys~s: A Second Course Academic Press, New York, 1972.
 
13
PAIGE, C.C Bidiagonahzation of matrices and solution of hnear equations. SIAM J. Numer. Anal. 11 (1974), 197-209.
 
14
John Franklin Palmer, II, Conjugate-direction methods and parallel-computing., 1974
 
15
RUHE, A. Implementation aspects of band Lanczos algorithms for computation of elgenvalues of large sparse symmetric matrices Rep., Dep of Mathematics, Umv. California, San Diego, Feb. 1978.
 
16
RUTISHAUSER, H. On Jacobi rotation patterns. In Proc. Syrup. Applled Math, vol. 15, 1963, pp. 219-239.
 
17
STEWART, G W. Error and perturbation bounds for subspaces associated with certain elgenvalue problems. SIAM Rev 15 (1973), 727-764
 
18
Richard Ray Underwood, An iterative block lanczos method for the solution of large sparse symmetric eigenproblems., 1975
 
19
Charles Francis Van Loan, Generalized singular values with algorithms and applications., 1973
 
20
J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988

CITED BY  2
 
Gang Wu, A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems, Journal of Computational and Applied Mathematics, v.205 n.1, p.343-363, August, 2007
E. M. Garzon , I. García, Parallel implementation of the Lanczos method for sparse matrices: analysis of data distributions, Proceedings of the 10th international conference on Supercomputing, p.294-300, May 25-28, 1996, Philadelphia, Pennsylvania, United States

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Sparse, structured, and very large systems (direct and iterative methods)

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices


General Terms:
Algorithms, Theory

Collaborative Colleagues:
Gene H. Golub: colleagues
Franklin T. Luk: colleagues
Michael L. Overton: colleagues

Peer to Peer - Readers of this Article have also read:

The ACM Portal is published by the Association for Computing Machinery. Copyright © 2009 ACM, Inc.
Terms of Usage   Privacy Policy   Code of Ethics   Contact Us

Useful downloads: Adobe Acrobat    QuickTime    Windows Media Player    Real Player
}, address = {New York, NY, USA}, author = {Golub, Gene H. and Luk, Franklin T. and Overton, Michael L.}, doi = {http://doi.acm.org/10.1145/355945.355946}, interhash = {b7d43137dfaa6351fc838c5c7a459a9f}, intrahash = {b6f719ab6d3027ab9967e80edd140959}, issn = {0098-3500}, journal = {ACM Trans. Math. Softw.}, number = 2, pages = {149--169}, publisher = {ACM}, title = {A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix}, url = {http://portal.acm.org/citation.cfm?id=355945.355946}, volume = 7, year = 1981 }