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Numerical Methods and their applications to Linear Algebra

By: Material type: TextTextPublication details: Ashland : Arcler Press, 2019.Description: 1 online resource (370 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 1773616552
  • 9781773616551
Subject(s): Genre/Form: Additional physical formats: Print version:: Numerical Methods and their applications to Linear Algebra.DDC classification:
  • 512.5 23
LOC classification:
  • QA185.D37
Online resources:
Contents:
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
IntroductionPreparations; 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 AnalysisCondition 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 EquationsAbstract; 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
AbstractIntroduction; 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
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Print version record.

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

IntroductionPreparations; 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 AnalysisCondition 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 EquationsAbstract; 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

AbstractIntroduction; 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

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