The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory [PDF]
Brazilian journal of physics, 2011 In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the solution of linear
AN Tikhonov +22 more
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A formula for the categorical magnitude in terms of the Moore-Penrose pseudoinverse [PDF]
Bulletin of the Belgian Mathematical Society Simon Stevin, 2023 The magnitude of finite categories is a generalization of the Euler characteristic. It is defined using the coarse incidence algebra of rational-valued functions on the given finite category, and a distinguished element in this algebra: the Dirichlet ...
Stephanie Chen, Juan Pablo Vigneaux
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The Use of the Moore-Penrose Pseudoinverse for Evaluating the RGA of Non-Square Systems [PDF]
Iraqi Journal of Computer, Communication, Control and System Engineering, 2021 A recently-derived alternative method for computing the relative gain array (RGA) for singular and/or non-square systems has been proposed, which provably guarantees unit invariance.
Rafal Qasim Al Yousuf, Jeffrey Uhlmann
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Stacked regression with a generalization of the Moore-Penrose Pseudoinverse [PDF]
Statistics in Transition New Series, 2017 In practice, it often happens that there are a number of classification methods. We are not able to clearly determine which method is optimal. We propose a combined method that allows us to consolidate information from multiple sources in a better ...
Tomasz Górecki, Maciej Łuczak
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Beyond Moore-Penrose Part II: The Sparse Pseudoinverse [PDF]
, 2017 This is the second part of a two-paper series on generalized inverses that minimize matrix norms. In Part II we focus on generalized inverses that are minimizers of entrywise p norms whose main representative is the sparse pseudoinverse for $p = 1$.
Dokmanić, Ivan, Gribonval, Rémi
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Characterization of Matrices Satisfying the Reverse Order Law for the Moore-Penrose Pseudoinverse [PDF]
Linear and multilinear algebraFor any complex matrix A, there exists a unique complex matrix $ {A}^\dag \! $ A†, called the Moore–Penrose pseudoinverse, such that the following conditions, known as the Penrose conditions, hold: $ A{A}^\dag \!A=A $ AA†A=A, $ {A}^\dag \!A{A}^\dag \!={A}
Oskar Kędzierski
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Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse [PDF]
International Journal of Applied Mathematics and Computer Sciences, 2013 The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when
Tomasz Górecki, Maciej Łuczak
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On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation [PDF]
Mathematical Problems in Engineering, 2019 Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas.
Marek Klimczak, Witold Cecot
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Comparing the Moore-Penrose Pseudoinverse and Gradient Descent for Solving Linear Regression Problems: A Performance Analysis [PDF]
arXiv.orgThis paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method.
Alex Adams
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General form of the Gauss-Seidel equation to linearly approximate the Moore-Penrose pseudoinverse in random non-square systems and high order tensors [PDF]
arXiv.orgThe Gauss-Seidel method has been used for more than 100 years as the standard method for the solution of linear systems of equations under certain restrictions.
Luis Saucedo‐Mora +1 more
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