Difference between revisions of "Pseudo-Inverse Algorithm"

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* <B>Example(s):</B>
 
* <B>Example(s):</B>
 
** 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 [[Weighted Pseudo-Inverse Algorithm]] ([[2015_AModifiedWeightedPseudoInverseC|Shao et al., 2015]]),
 
** a [[Online PseudoInverse Update Method (OPIUM) Algorithm]] ([[2013_2013SpecialIssueLearningthePseu|Tapson & Schaik, 2013]]),
 
** a [[Online PseudoInverse Update Method (OPIUM) Algorithm]] ([[2013_2013SpecialIssueLearningthePseu|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)]]),
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* ([[2016_EfficientGeneralizedInverseforS|Kadiam Bose & Nguyen, 2016]]) ⇒ [[author::S. Kadiam Bose]], and [[author::D. T. Nguyen]]. ([[year::2016]]). &ldquo;[https://www.scirp.org/Journal/PaperInformation.aspx?PaperID=62628 Efficient Generalized Inverse for Solving Simultaneous Linear Equations].&rdquo; In: Journal of Applied Mathematics and Physics, 4. [http://dx.doi.org/10.4236/jamp.2016.41003 doi:10.4236/jamp.2016.41003]  
 
* ([[2016_EfficientGeneralizedInverseforS|Kadiam Bose & Nguyen, 2016]]) ⇒ [[author::S. Kadiam Bose]], and [[author::D. T. Nguyen]]. ([[year::2016]]). &ldquo;[https://www.scirp.org/Journal/PaperInformation.aspx?PaperID=62628 Efficient Generalized Inverse for Solving Simultaneous Linear Equations].&rdquo; In: Journal of Applied Mathematics and Physics, 4. [http://dx.doi.org/10.4236/jamp.2016.41003 doi:10.4236/jamp.2016.41003]  
 
** QUOTE: The [[Pseudo-Inverse Matrix|generalized (or pseudo) inverse of a matrix]] is an extension of the [[Square Matrix|ordinary/regular square]] ([[Non-Singular Matrix|non-singular]]) [[matrix inverse]], which can be applied to any [[matrix]] (such as [[Singular Matrix|singular]], [[Rectangular Matrix|rectangular]] etc.). The [[generalized inverse]] has numerous important [[engineering]] and [[science]]s [[application]]s. Over the past decades, [[generalized inverse]]s of [[matrice]]s and its [[application]]s have been investigated by many [[researcher]]s [[2016_EfficientGeneralizedInverseforS#References|1-6]]. [[Generalized inverse]] is also known as “[[Moore-Penrose inverse]]” or “[[g-inverse]]” or “[[pseudo-inverse]]” etc. <P>[[2016_EfficientGeneralizedInverseforS|In this paper we]] introduce an efficient (in terms of [[computational time]] and [[computer memory requirement]]) [[generalized inverse formulation]] to solve [[SLE]] with full or [[deficient rank]] of the [[coefficient matrix]]. The [[coefficient matrix]] can be [[Singular Matrix|singular/non-singular]], [[Symmmetric Matrix|symmetric/unsymmetric]], or [[Square Matrix|square]]/[[Rectangular Matrix|rectangular]]. Due to popular [[MATLAB]] [[software]], which is widely accepted by [[researcher]]s and [[educator]]s worldwide, the developed [[code]] from this work is written in [[MATLAB language]].
 
** QUOTE: The [[Pseudo-Inverse Matrix|generalized (or pseudo) inverse of a matrix]] is an extension of the [[Square Matrix|ordinary/regular square]] ([[Non-Singular Matrix|non-singular]]) [[matrix inverse]], which can be applied to any [[matrix]] (such as [[Singular Matrix|singular]], [[Rectangular Matrix|rectangular]] etc.). The [[generalized inverse]] has numerous important [[engineering]] and [[science]]s [[application]]s. Over the past decades, [[generalized inverse]]s of [[matrice]]s and its [[application]]s have been investigated by many [[researcher]]s [[2016_EfficientGeneralizedInverseforS#References|1-6]]. [[Generalized inverse]] is also known as “[[Moore-Penrose inverse]]” or “[[g-inverse]]” or “[[pseudo-inverse]]” etc. <P>[[2016_EfficientGeneralizedInverseforS|In this paper we]] introduce an efficient (in terms of [[computational time]] and [[computer memory requirement]]) [[generalized inverse formulation]] to solve [[SLE]] with full or [[deficient rank]] of the [[coefficient matrix]]. The [[coefficient matrix]] can be [[Singular Matrix|singular/non-singular]], [[Symmmetric Matrix|symmetric/unsymmetric]], or [[Square Matrix|square]]/[[Rectangular Matrix|rectangular]]. Due to popular [[MATLAB]] [[software]], which is widely accepted by [[researcher]]s and [[educator]]s worldwide, the developed [[code]] from this work is written in [[MATLAB language]].
 
+
=== 2015 ===
 +
* ([[2015_AModifiedWeightedPseudoInverseC|Shao et al., 2015]]) ⇒ [[author::Xingyue Shao]], [[author::Zixuan Liang]], [[author::Bai Chen]], and [[author::Cunjia Liu]]. ([[year::2015]]). &ldquo;[https://www.semanticscholar.org/paper/A-modified-weighted-pseudo-inverse-control-using-Shao-Liang/d1e4312010d7473432db5e74c2db5b2a6c926d04 A Modified Weighted Pseudo-inverse Control Allocation Using Genetic Algorithm].&rdquo; In: Proceedings of 34th Chinese Control Conference (CCC 2015).. [http://dx.doi.org/10.1109/ChiCC.2015.7260507 doi:10.1109/ChiCC.2015.7260507]
 
=== 2013 ===
 
=== 2013 ===
 
* ([[2013_2013SpecialIssueLearningthePseu|Tapson & Van Schaik, 2013]]) ⇒ [[author::J. Tapson]], and [[author::A. Van Schaik]]. ([[year::2013]]). &ldquo;[https://www.westernsydney.edu.au/__data/assets/pdf_file/0003/783156/Tapson,_van_Schaik_-_2013_-_Learning_the_pseudoinverse_solution_to_network_weights.pdf 2013 Special Issue: Learning the Pseudoinverse Solution to Network Weights].&rdquo; In: Neural Networks Journal, 45. [http://dx.doi.org/10.1016/j.neunet.2013.02.008 doi:10.1016/j.neunet.2013.02.008]
 
* ([[2013_2013SpecialIssueLearningthePseu|Tapson & Van Schaik, 2013]]) ⇒ [[author::J. Tapson]], and [[author::A. Van Schaik]]. ([[year::2013]]). &ldquo;[https://www.westernsydney.edu.au/__data/assets/pdf_file/0003/783156/Tapson,_van_Schaik_-_2013_-_Learning_the_pseudoinverse_solution_to_network_weights.pdf 2013 Special Issue: Learning the Pseudoinverse Solution to Network Weights].&rdquo; In: Neural Networks Journal, 45. [http://dx.doi.org/10.1016/j.neunet.2013.02.008 doi:10.1016/j.neunet.2013.02.008]

Revision as of 14:05, 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

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1966

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1955