# 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+ | + | * [[Google Scholar]]: 206 Citations [http://scholar.google.com/scholar?q=%222008%22+Fast+Computation+of+Moore-Penrose+Inverse+Matrices+] |

− | + | * [[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 == | ||

+ | # 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. | ||

{{#ifanon:| | {{#ifanon:| | ||

## Latest revision as of 12:48, 13 July 2019

- (Courrieu, 2008) ⇒ Pierre Courrieu. (2008). “Fast Computation of Moore-Penrose Inverse Matrices .” In: Neural Information Processing - Letters and Reviews Journal, 8.

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

## Notes

## Cited By

- Google Scholar: 206 Citations [1]
- Semantic Scholar: 80 Citations [2]

## Quotes

### Author Keywords

- Rank Deficient Least Square Systems; Moore-Penrose Inverse; Pseudoinverse; Generalized Inverse; Neural Learning; Minimum-norm Synaptic Weight Vectors; Regularization.

### 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

- 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.;

Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
---|---|---|---|---|---|---|---|---|---|---|

2008 FastComputationofMoorePenroseIn | Pierre Courrieu | Fast Computation of Moore-Penrose Inverse Matrices | 2008 |

Author | Pierre Courrieu + |

title | Fast Computation of Moore-Penrose Inverse Matrices + |

year | 2008 + |