Difference between revisions of "Pseudo-Inverse Algorithm"

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** a [[Online PseudoInverse Update Method (OPIUM) Algorithm]] ([[Tapson & Schaik, 2013]]),
 
** a [[Online PseudoInverse Update Method (OPIUM) Algorithm]] ([[Tapson & Schaik, 2013]]),
 
** a [[Courrieu's Fast Moore-Penrose Inverse Algorithm]] ([[2008_FastComputationofMoorePenroseIn|Courrieu (2008)]]),
 
** a [[Courrieu's Fast Moore-Penrose Inverse Algorithm]] ([[2008_FastComputationofMoorePenroseIn|Courrieu (2008)]]),
** a [[Fast B-Spline Pseudo-inversion Algorithm]] ([[Tristan & Arribas, 2007]]),
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** a [[Fast B-Spline Pseudo-inversion Algorithm]] ([[2007_AFastBSplinePseudoInversionAlgo|Tristan & Arribas, 2007]]),
 
** a [[Herron's Pseudo-Inverse Algorithm]] ([[#1966|Herron, 1966]]).
 
** a [[Herron's Pseudo-Inverse Algorithm]] ([[#1966|Herron, 1966]]).
 
* <B>Counter-Example(s):</B>
 
* <B>Counter-Example(s):</B>
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* ([[2008_FastComputationofMoorePenroseIn|Courrieu, 2008]]) ⇒ [[author::Pierre Courrieu]]. ([[year::2008]]). &ldquo;[https://arxiv.org/pdf/0804.4809.pdf Fast Computation of Moore-Penrose Inverse Matrices ].&rdquo; In: Neural Information Processing - Letters and Reviews  Journal, 8.  
 
* ([[2008_FastComputationofMoorePenroseIn|Courrieu, 2008]]) ⇒ [[author::Pierre Courrieu]]. ([[year::2008]]). &ldquo;[https://arxiv.org/pdf/0804.4809.pdf Fast Computation of Moore-Penrose Inverse Matrices ].&rdquo; In: Neural Information Processing - Letters and Reviews  Journal, 8.  
 
** QUOTE: The [[Moore-Penrose inverse]], also called [[Pseudoinverse]], or [[Generalized Inverse]], allows for solving [[least square system]]s, even with [[rank deficient matrice]]s, in such a way that each [[column vector]] of the solution has a [[minimum norm]], which is the desired property stated above.
 
** QUOTE: The [[Moore-Penrose inverse]], also called [[Pseudoinverse]], or [[Generalized Inverse]], allows for solving [[least square system]]s, even with [[rank deficient matrice]]s, in such a way that each [[column vector]] of the solution has a [[minimum norm]], which is the desired property stated above.
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=== 2007 ===
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* ([[2007_AFastBSplinePseudoInversionAlgo|Tristán & Arribas, 2007]]) ⇒ [[author::Antonio Tristán]], and [[author::Juan Ignacio Arribas]]. ([[year::2007]]). &ldquo;[https://link.springer.com/chapter/10.1007%2F978-3-540-74272-2_95 A Fast B-spline Pseudo-inversion Algorithm for Consistent Image Registration].&rdquo; In: [[Proceedings of the 12th international conference on Computer analysis of images and patterns]]. ISBN:978-3-540-74271-5
  
 
=== 1966 ===
 
=== 1966 ===

Revision as of 13:12, 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

2007

1966

1965

1955