Difference between revisions of "2008 FastComputationofMoorePenroseIn"

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== Cited By ==
 
== Cited By ==
* http://scholar.google.com/scholar?q=%222008%22+Fast+Computation+of+Moore-Penrose+Inverse+Matrices+
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* [[Google Scholar]]: 206 Citations [http://scholar.google.com/scholar?q=%222008%22+Fast+Computation+of+Moore-Penrose+Inverse+Matrices+]
 
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* [[Semantic Scholar]]:  80 Citations [https://www.semanticscholar.org/paper/Fast-Computation-of-Moore-Penrose-Inverse-Matrices-Courrieu/558302694056d18dfe65d5fd68a1f296f70e0930#citingPapers]
  
 
== Quotes ==
 
== Quotes ==
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== References ==
 
== References ==
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# F. Girosi and T. Poggio, “Networks and the best approximation property,” Biological Cybernetics, 63, pp. 169-176, 1990.
 +
# T. Poggio andF. Girosi, “Networks for approximation and learning,” Proceedings of the IEEE, 78(9), pp. 1481-1497, 1990.
 +
# A. B. Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications, (2nd ed.), New-York, Springer, 2003.
 +
# M.A. Rakha, “On the Moore-Penrose generalized inverse matrix,” Applied Mathematics and Computation, 158, pp. 185-200, 2004.
 +
# Y. Wei and G. Wang, “PCR algorithm for parallel computing minimum-norm (T) least-squares (S) solution of inconsistent linear equations,” Applied Mathematics and Computation, 133, pp. 547-557, 2002.
 +
# P. Courrieu, “Straight monotonic embedding of data sets in Euclidean spaces,” Neural Networks, 15, pp. 1185-1196, 2002.
 +
# P. Courrieu, “Solving time of least square systems in Sigma-Pi unit networks,” Neural Information Processing – Letters and Reviews, 4(3), pp. 39-45, 2004.
 +
# T.N.E. Greville, “Some applications of the pseudoinverse of a matrix,” SIAM Review, 2, pp. 15-22, 1960.
 +
# C.A. Micchelli, “Interpolation of scattered data: distance matrices and conditionally positive definite functions,” Constructive Approximation, 2, pp. 11-22, 1986.
 +
# S.K. Sin and R.J.P. DeFigueiredo, “Efficient learning procedures for optimal interpolative nets,” Neural Networks, 6, pp. 99-113, 1993.
 
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Latest revision as of 12:48, 13 July 2019

Subject Headings: Pseudo-Inverse Algorithm; Pseudo-Inverse Matrix.

Notes

Cited By

Quotes

Author Keywords

Abstract

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for computing Moore-Penrose inverse matrices. In this paper, an algorithm based on a full rank Cholesky factorization is proposed. The resulting pseudoinverse matrices are similar to those provided by other algorithms. However the computation time is substantially shorter, particularly for large systems.


References

  1. F. Girosi and T. Poggio, “Networks and the best approximation property,” Biological Cybernetics, 63, pp. 169-176, 1990.
  2. T. Poggio andF. Girosi, “Networks for approximation and learning,” Proceedings of the IEEE, 78(9), pp. 1481-1497, 1990.
  3. A. B. Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications, (2nd ed.), New-York, Springer, 2003.
  4. M.A. Rakha, “On the Moore-Penrose generalized inverse matrix,” Applied Mathematics and Computation, 158, pp. 185-200, 2004.
  5. Y. Wei and G. Wang, “PCR algorithm for parallel computing minimum-norm (T) least-squares (S) solution of inconsistent linear equations,” Applied Mathematics and Computation, 133, pp. 547-557, 2002.
  6. P. Courrieu, “Straight monotonic embedding of data sets in Euclidean spaces,” Neural Networks, 15, pp. 1185-1196, 2002.
  7. P. Courrieu, “Solving time of least square systems in Sigma-Pi unit networks,” Neural Information Processing – Letters and Reviews, 4(3), pp. 39-45, 2004.
  8. T.N.E. Greville, “Some applications of the pseudoinverse of a matrix,” SIAM Review, 2, pp. 15-22, 1960.
  9. C.A. Micchelli, “Interpolation of scattered data: distance matrices and conditionally positive definite functions,” Constructive Approximation, 2, pp. 11-22, 1986.
  10. S.K. Sin and R.J.P. DeFigueiredo, “Efficient learning procedures for optimal interpolative nets,” Neural Networks, 6, pp. 99-113, 1993.;


 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
2008 FastComputationofMoorePenroseInPierre CourrieuFast Computation of Moore-Penrose Inverse Matrices2008
AuthorPierre Courrieu +
titleFast Computation of Moore-Penrose Inverse Matrices +
year2008 +