Difference between revisions of "Pseudo-Inverse Algorithm"

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* <B>AKA:</B> [[Pseudo-Inverse]], [[Pseudoinverse Algorithm]],  [[Moore-Penrose Inverse Algorithm]], [[Generalized Inverse Algorithm]].
 
* <B>AKA:</B> [[Pseudo-Inverse]], [[Pseudoinverse Algorithm]],  [[Moore-Penrose Inverse Algorithm]], [[Generalized Inverse Algorithm]].
 
* <B>Example(s):</B>
 
* <B>Example(s):</B>
** a [[Weighted Pseudo-Inverse Algorithm]],
 
 
** a [[Bose-Nguyen Generalized Inverse Algorithm]] ([[2016_EfficientGeneralizedInverseforS|Bose & Nguyen, 2016]]),
 
** a [[Bose-Nguyen Generalized Inverse Algorithm]] ([[2016_EfficientGeneralizedInverseforS|Bose & Nguyen, 2016]]),
 +
** a [[Weighted Pseudo-Inverse Algorithm]] ([[Shao et al., 2015]]),
 +
** a [[Online PseudoInverse Update Method (OPIUM) Algorithm]] ([[Tapson & Schaik, 2013]]),
 +
** a [[Courrieu's Fast Moore-Penrose Inverse Algorithm]] ([[2008_FastComputationofMoorePenroseIn|Courrieu (2008)]]),
 
** a [[Fast B-Spline Pseudo-inversion Algorithm]] ([[Tristan & Arribas, 2007]]),
 
** a [[Fast B-Spline Pseudo-inversion Algorithm]] ([[Tristan & Arribas, 2007]]),
 +
** a [[Herron's Pseudo-Inverse Algorithm]] ([[Herron, 1966]]).
 
* <B>Counter-Example(s):</B>
 
* <B>Counter-Example(s):</B>
 
** a [[Matrix Multiplication Algorithm]] such as:
 
** a [[Matrix Multiplication Algorithm]] such as:
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__NOTOC__
 
__NOTOC__
 
[[Category:Concept]]
 
[[Category:Concept]]
[[Categpry:Mathematics]]
+
[[Category:Mathematics]]
 
[[Category:Machine Learning]]
 
[[Category:Machine Learning]]

Revision as of 12:40, 13 July 2019

A Pseudo-Inverse Algorithm is a Matrix Decomposition Algorithm that can solve a least square system such that each column vector of the solution has a minimum norm.



References

2019

  1. Moore, E. H. (1920). "On the reciprocal of the general algebraic matrix". Bulletin of the American Mathematical Society. 26 (9): 394–95. doi:10.1090/S0002-9904-1920-03322-7.
  2. Bjerhammar, Arne (1951). "Application of calculus of matrices to method of least squares; with special references to geodetic calculations". Trans. Roy. Inst. Tech. Stockholm. 49.
  3. Penrose, Roger (1955). "A generalized inverse for matrices". Proceedings of the Cambridge Philosophical Society. 51 (3): 406–13. doi:10.1017/S0305004100030401.

2016

2008

1965

1955