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  • Generalized Matrix Inversion: A Machine Learning Approach

    Series series Artificial Intelligence (R0)
    This book presents a comprehensive exploration of the dynamical system approach in numerical linear algebra, with a special focus on computing generalized inverses, solving systems of linear equations, and addressing linear matrix equations. Bridging four major scientific domains—numerical linear algebra, recurrent neural networks (RNNs), dynamical systems, and unconstrained nonlinear optimization ... Read more

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  • Theory and Computation of Complex Tensors and its Applications

    Series series Mathematics and Statistics (R0)
    The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a ... Read more

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  • Numerical And Symbolic Computations Of Generalized Inverses

    We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed ... Read more

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  • Theory and Computation of Tensors

    Multi-Dimensional Arrays

    Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear ... Read more

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  • Generalized Inverses: Theory and Computations

    Series series Mathematics and Statistics (R0)
    This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics.It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the ... Read more

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  • Algebraic Properties of Generalized Inverses

    Series series Mathematics and Statistics (R0)
    This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses.Particular emphasis is placed on the existence of Drazin invertible completions ... Read more

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