Fundamentals of Matrix Computations(2020)[Moreira][ 9781774073773]

Fundamentals of Matrix Computations deals with the concept of matrix computations, a technique of singular value homogenization and its application in medical therapy. It consists of modern iterative methods to generalize the issues associated with singular-value homogenization. It provides the reader with the understanding of matrix computations and preconditioning technique of singular value homogenization so as to analyze its potential applications in the field of medical therapy and the use of efficient numerical methods so as to solve the problems linked with nonlinear singular boundary value by using improved differential transform method. This book also discusses about blind distributed estimation algorithms for adaptive networks, a dft-based approximate eigenvalue and singular value decomposition of polynomial matrices, sparse signal subspace decomposition based on adaptive over-complete dictionary, lower bounds for the low-rank matrix approximation and a semi-smoothing augmented lagrange multiplier algorithm for low-rank toeplitz matrix completion. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 Singular Value Homogenization: a Simple Preconditioning Technique for Linearly Constrained Optimization and its Potential Applications in Medical Therapy Abstract Introduction Preliminaries Singular Value Homogenization Numerical Experiments Conclusion Acknowledgements Authors’ Contributions References Chapter 2 Perturbation Bounds for Eigenvalues of Diagonalizable Matrices and Singular Values Abstract Introduction Perturbation Bounds For Eigenvalues of Diagonalizable Matrices Perturbation Bounds For Singular Values Acknowledgements Authors’ Contributions References Chapter 3 New Iterative Methods for Generalized Singular-value Problems Abstract Introduction Preparations Numerical Experiments Conclusions References Chapter 4 Blind Distributed Estimation Algorithms for Adaptive Networks Abstract Introduction Problem Statement Blind Estimation Algorithm Proposed Recursive Blind Estimation Algorithms Complexity of The Recursive Algorithms Simulations And Results Conclusion Acknowledgments References Chapter 5 A DFT-based Approximate Eigenvalue and Singular Value Decomposition of Polynomial Matrices Abstract Introduction Problem Formulation Spectral Majorized Decomposition Versus Smooth Decomposition Finite Duration Constraint Gradient Descent Solution Simulation Results Conclusion References Chapter 6 Canonical Polyadic Decomposition of Third-order Semi-nonnegative Semi-symmetric Tensors using LU and QR Matrix Factorizations Abstract Introduction Multilinear Algebra Prerequisites and Problem Statement Methods Simulation Results Conclusions References Chapter 7 Sparse Signal Subspace Decomposition based on Adaptive Over-complete Dictionary Abstract Introduction Review of PCA and Sparse Coding Methods The Proposed Sparse Subspace Decomposition Results and Discussion Conclusions Acknowledgements Authors’ Contributions References Chapter 8 Lower Bounds for the Low-rank Matrix Approximation Abstract Introduction Preliminaries Experiments Conclusion Acknowledgements Authors’ Contributions References Chapter 9 A Reduced-rank Approach for Implementing Higher-order Volterra Filters Abstract Introduction Volterra Filters And Reduced-Rank Implementations Novel Reduced-Rank Approach For Implementing Volterra Filters Simulation Results Conclusions Acknowledgements References Chapter 10 A Semi-smoothing Augmented Lagrange Multiplier Algorithm for Low-rank Toeplitz Matrix Completion Abstract Introduction Preliminaries Algorithms Convergence Analysis Numerical Experiments Concluding Remarks Acknowledgements Authors’ Contributions References Chapter 11 Singular Spectrum-based MatrixCompletion for Time Series Recovery and Prediction Abstract Introduction Related Work Analysis of Time Series Data Low-Rank Matrix Completion The SS-MC Algorithm Experimental Results Conclusions Acknowledgements References Chapter 12 An Effective Numerical Method to Solve a Class of Nonlinear Singular Boundary Value Problems using improved Differential Transform Method Abstract Background Adomian Polynomial And Differential Transform Method of Solution of Sbvps (1–3) Numerical Examples Conclusion Authors’ Contributions Acknowlegements References Index Back Cover Examines the concept of matrix computations, a technique of singular value homogenization and its application in medical therapy. The book consists of modern iterative methods to generalize the issues associated with singular-value homogenization. It also provides an understanding of matrix computations.