Numerical Methods and their applications to Linear Algebra

Numerical Methods and their applications to Linear Algebra takes into account various dimensions of linear algebra related to the numerical methods. It includes new iterative methods for generalized singular-value problems and perturbation analysis of the stochastic algebraic Riccati equation. Provide the reader with the insights into the development of various numerical methods adopted for linear algebra, so as to understand and gain practical knowledge of modern computational techniques for the numerical solution of linear algebra. Cover Half Title Page Title Page Copyright Page Declaration About the Editor Table of Contents List of Contributors List of Abbreviations Preface SECTION I Chapter 1 Distributed Gram-Schmidt Orthogonalization With Simultaneous Elements Refinement Abstract Introduction Average Consensus Algorithm Qr Factorization Distributed Classical Gram-Schmidt With Simultaneous Elements Refinement Performance of DS-CGS Conclusions Endnotes Appendix: Local Algorithm Acknowledgements References Chapter 2 New Iterative Methods For Generalized Singular-Value Problems Abstract Introduction Preparations A New Iterative Method For GSVD Numerical Experiments Conclusions References Chapter 3 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 Untitled SECTION II Chapter 4 Perturbation Analysis of the Stochastic Algebraic Riccati Equation Abstract Introduction Perturbation Equation Perturbation Bounds Stability Analysis Condition Number of The Sare Numerical Experiment Conclusion Appendix Acknowledgements References Chapter 5 A Tridiagonal Matrix Construction By The Quotient Difference Recursion Formula In The Case Of Multiple Eigenvalues Abstract Introduction Some Properties For The QD Recursion Formula Tridiagonal Matrix Associated With General Matrix Minimal Polynomial of Tridiagonal Matrix Procedure For Constructing Tridiagonal Matrix And Its Examples Conclusion Acknowledgements References SECTION III Chapter 6 Stability Analysis of Additive Runge-Kutta Methods For Delay-Integro-Differential Equations Abstract Introduction The Numerical Methods Stability Analysis Conclusion Acknowledgments References Chapter 7 A Numerical Method For Partial Differential Algebraic Equations Based On Differential Transform Method Abstract Introduction Indexes of Partial Differential Algebraic Equation Two-Dimensional Differential Transform Method Application Conclusion References SECTION IV Chapter 8 Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPS Abstract Introduction Linear Algebra Algorithm Selection Process of Dynamic Range Estimation Bit-True Fixed Point Simulation Algorithm Porting To A Target DSP Results Conclusion References Chapter 9 Performance Versus Energy Consumption of Hyperspectral Unmixing Algorithms on Multi-Core Platforms Abstract Introduction Spectral Unmixing Modules Multi-Core Implementations Experimental Results Conclusions Acknowledgements References SECTION V Chapter 10 A Unified View Of Adaptive Variable-Metric Projection Algorithms Abstract Introduction Adaptive Projected Subgradient Method: Asymptotic Minimization of A Sequence of Cost Functions Variable-Metric Extension of APSM A Deterministic Analysis Numerical Examples Conclusion Appendices Acknowledgment References Chapter 11 New Techniques For Linear Arithmetic: Cubes And Equalities Abstract Introduction Preliminaries Fitting Cubes Into Polyhedra Fast Cube Tests Experiments From Cubes To Equalities Implementation And Application Conclusions Acknowledgements References Index

Numerical Methods and their applications to Linear Algebra takes into account variousdimensions of linear algebra related to the numerical methods. It includes new iterativemethods for generalized singular-value problems and perturbation analysis of the stochasticalgebraic Riccati equation. Provide the reader with the insights into the developmentof various numerical methods adopted for linear algebra, so as to understandand gain practical knowledge of modern computational techniques for the numericalsolution of linear algebra.