Fundamentals of Matrix Computations

✍ Scribed by Olga Moreira (editor)

• Publisher: Arcler Press
• Year: 2020
• Tongue: English
• Leaves: 338
• Category: Library

✦ Table of Contents

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
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