Generalized Inverses: Algorithms and Applications

Name: Generalized Inverses: Algorithms and Applications
Brand: Nova Science Publishers Inc
Price: 240.99 EUR
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Kyrchei Ivan(Herausgeber*in)

Nova Science Publishers Inc

Erschienen am 4. Januar 2022

288 Seiten

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978-1-68507-513-2 (ISBN)

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Intro
GENERALIZED INVERSESALGORITHMSAND APPLICATIONS
GENERALIZED INVERSESALGORITHMSAND APPLICATIONS
Contents
PREFACE
Chapter 1A SURVEY OF COMPOSITE GENERALIZEDINVERSES
Abstract
1. INTRODUCTION
2. OMP INVERSES
2.1. Characterizations and Representations of theOMP Inverse
2.2. Representations of the OMP Inverse
3. MPO INVERSES
3.1. Characterizations of the MPO Inverse
3.2. Representations of the MPO Inverse
4. MPOMP INVERSES
4.1. Characterizations of the MPOMP Inverse
4.2. Representations of the MPOMP Inverse
5. EXAMPLES
CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Chapter 2THE BT INVERSE
Abstract
1. INTRODUCTION
2. PRELIMINARIES
3. DEFINITION, EXISTENCE AND UNIQUENESS
4. THE BT INVERSE AND THE HARTWIGSPINDELB¨OCK DECOMPOSITIONIn
5. THE BT INVERSE AND THE CORE EPDECOMPOSITION
6. THE BT ORDER
REFERENCES
Chapter 3PERTURBATION ESTIMATIONSFOR THE DRAZIN INVERSE
Abstract
1. INTRODUCTION AND PRELIMINARIES
2. GEOMETRICAL CONDITIONS ON THE ACUTE PERTURBATION
3. EXAMPLE
CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Chapter 4CRAMER'S RULES FOR SYSTEMS OFQUATERNION MATRIX EQUATIONS
Abstract
1. INTRODUCTION
2. PRELIMINARIES
2.1. Elements of the Theory of Row-Column Determinants
2.2. Determinantal Representations of the Moore-Penrose In-verses with Applications to the Twos-Sided Matrix Equa-tion
3. CRAMER'S RULE FOR THE SYSTEM (1.1)
4. CRAMER'S RULES FOR PARTIAL CASESOF (1.1)
5. CRAMER'S RULES FOR THE SOLUTIONAND HERMITIAN SOLUTION TO THESYSTEM WITH -HERMICITY
6. CRAMER'S RULE FOR THE SYSTEMWITH -HERMISITY
7. EXAMPLES
CONCLUSION
REFERENCES
Chapter 5SOLUTIONS TO SOME SYLVESTER-TYPETENSOR EQUATIONS UNDER T-PRODUCT
Abstract
1. INTRODUCTION
2. PRELIMINARIES
3. THE GENERAL SOLUTION TO THE TENSOR EQUATION (1)
4. THE SYMMETRIC SOLUTION TO THE TENSOR EQUATION (2)
5. THE GENERAL SOLUTION TO THE SYSTEM (3)
CONCLUSION
REFERENCES
Chapter 6TOWARDS HIGHER ORDERDYNAMICAL SYSTEMS
Abstract
1. INTRODUCTION
2. PRELIMINARIES
3. HIGHER-ORDER ZNN FOR COMPUTING THEMATRIX INVERSE
3.1. Integration-Enhanced Noise-Tolerant ZNNpH Dynamics
4. HIGHER-ORDER ZNN FOR COMPUTINGTHE MP INVERSE
5. HIGHER-ORDER IENH-ZNN FORCOMPUTING THE MP INVERSE
6. SIMULATION EXAMPLES
6.1. Analyzing the Examples
CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Chapter 7WEIGHTED MOORE-PENROSE INVERSEWITH INDEFINITE SINGULAR WEIGHTS
ABSTRACT
INTRODUCTION
2. NOTATION, DEFINITIONS, FACTS OF COMMONKNOWLEDGE AND AUXILIARY STATEMENTS
3. THEOREMS ON EXISTENCE AND UNIQUENESS
4. EXPANSION OF WEIGHTED PSEUDOINVERSEMATRICES IN THE FORM OF MATRIX POWER SERIESAND MATRIX PRODUCTS
5. CONSTRUCTION OF ITERATIVE PROCESSES FORTHE EVALUATION OF WEIGHTEDPSEUDOINVERSE MATRICES
CONCLUSION
REFERENCES
EDITOR CONTACT INFORMATION
INDEX
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