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]] ([[2007_AFastBSplinePseudoInversionAlgo|Tristan & Arribas, 2007]]),
 
** a [[Fast B-Spline Pseudo-inversion Algorithm]] ([[2007_AFastBSplinePseudoInversionAlgo|Tristan & Arribas, 2007]]),
** a [[Herron's Pseudo-Inverse Algorithm]] ([[#1966|Herron, 1966]]).
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** a [[Herron's Pseudo-Inverse Algorithm]] ([[#1966|Herron, 1966]]),
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** a [[Greville's Pseudo-Inverse Algorithm]] ([[#1960|Greville, 1960]]).
 
* <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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=== 1965 ===
 
=== 1965 ===
 
* (Golub & Kahan, 1965) ⇒ G. Golub and W. Kahan. (1965). “</i>[http://www.jstor.org/stable/2949777 Calculating the Singular Values and Pseudo-Inverse of a Matrix].” In: Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, 2(2).
 
* (Golub & Kahan, 1965) ⇒ G. Golub and W. Kahan. (1965). “</i>[http://www.jstor.org/stable/2949777 Calculating the Singular Values and Pseudo-Inverse of a Matrix].” In: Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, 2(2).
 
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=== 1960 ===
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* (Greville,1960) &rArr; [[T. N. E. Greville]] (1960). [http://benisrael.net/GREVILLE-GI-60.pdf "Some applications of the pseudoinverse of a matrix"]. [[SIAM review]], 2(1), 15-22.
 
=== 1955 ===
 
=== 1955 ===
 
* (Penrose, 1955) ⇒  [[Roger Penrose]] (1955, July). [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.5377&rep=rep1&type=pdf "A generalized inverse for matrices"]. In [[Mathematical proceedings of the Cambridge philosophical society]] (Vol. 51, No. 3, pp. 406-413). Cambridge University Press.
 
* (Penrose, 1955) ⇒  [[Roger Penrose]] (1955, July). [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.5377&rep=rep1&type=pdf "A generalized inverse for matrices"]. In [[Mathematical proceedings of the Cambridge philosophical society]] (Vol. 51, No. 3, pp. 406-413). Cambridge University Press.

Revision as of 13:45, 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

2013

2008

2007

1966

1965

1960

1955