Difference between revisions of "Pseudo-Inverse Algorithm"

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** 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]]),
 
** a [[Fast B-Spline Pseudo-inversion Algorithm]] ([[Tristan & Arribas, 2007]]),
** a [[Herron's Pseudo-Inverse Algorithm]] ([[Herron, 1966]]).
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** a [[Herron's Pseudo-Inverse Algorithm]] ([[#1966|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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* ([[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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=== 1966 ===
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* (Herron, 1966) ⇒  [[Christopher R. Herron]] (1966). [https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670014642.pdf "Computing the pseudo-inverse"].
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** QUOTE: An [[orthogonalization algorithm]] for producing the [[pseudoinverse]] of a [[matrix]] is described, and a [[FORTRAN]] [[program]] which realizes the [[algorithm]] is given in detail.
  
 
=== 1965 ===
 
=== 1965 ===

Revision as of 13:00, 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

1966

1965

1955