Holdings: Control perspectives on numerical algorithms and matrix problems

Control perspectives on numerical algorithms and matrix problems:

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Bibliographic Details
Main Authors:	Bhaya, Amit (Author), Kaszkurewicz, Eugenius (Author)
Format:	Book
Language:	English
Published:	Philadelphia Society for Industrial and Applied Mathematics 2006
Series:	Advances in design and control
Subjects:	Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie Numerische Mathematik
Online Access:	Inhaltsverzeichnis
Physical Description:	XXV, 272 S. Ill., graph. Darst.
ISBN:	0898716020

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MARC


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Record in the Search Index

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adam_text	CONTROL PERSPECTIVES ON NUMERICAL ALGORITHMS AND MATRIX PROBLEMS AMIT BHAYA EUGENIUS KASZKUREWICZ FEDERAL UNIVERSITY OF RIO DE JANEIRO RIO DE JANEIRO, BRAZIL SIAJTL SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA CONTENTS LIST OF FIGURES XI LIST OF TABLES XVII PREFACE XIX 1 BRIEF REVIEW OF CONTROL AND STABILITY THEORY 1 1.1 CONTROL THEORY BASICS 1 1.1.1 FEEDBACK CONTROL TERMINOLOGY 1 1.1.2 PID CONTROL FOR DISCRETE-TIME SYSTEMS 6 1.2 OPTIMAL CONTROL THEORY 8 1.3 LINEAR SYSTEMS, TRANSFER FUNCTIONS, REALIZATION THEORY 10 1.4 BASICS OF STABILITY OF DYNAMICAL SYSTEMS 15 1.5 VARIABLE STRUCTURE CONTROL SYSTEMS 27 1.6 GRADIENT DYNAMICAL SYSTEMS 31 1.6.1 NONSMOOTH GDSS: PERSIDSKII-TYPE RESULTS 35 1.7 NOTES AND REFERENCES 38 2 ALGORITHMS AS DYNAMICAL SYSTEMS WITH FEEDBACK 41 2.1 CONTINUOUS-TIME DYNAMICAL SYSTEMS THAT FIND ZEROS 42 2.2 ITERATIVE ZERO FINDING ALGORITHMS AS DISCRETE-TIME DYNAMICAL SYSTEMS 56 2.3 ITERATIVE METHODS FOR LINEAR SYSTEMS AS FEEDBACK CONTROL SYSTEMS . . 70 2.3.1 CLF/LOC DERIVATION OF MINIMAL RESIDUAL AND KRYLOV SUBSPACE METHODS 75 2.3.2 THE CONJUGATE GRADIENT METHOD DERIVED FROM A PROPORTIONAL-DERIVATIVE CONTROLLER 77 2.3.3 CONTINUOUS ALGORITHMS FOR FINDING OPTIMA AND THE CONTINUOUS CONJUGATE GRADIENT ALGORITHM 85 2.4 NOTES AND REFERENCES 90 3 OPTIMAL CONTROL AND VARIABLE STRUCTURE DESIGN OF ITERATIVE METHODS 93 3.1 OPTIMALLY CONTROLLED ZERO FINDING METHODS 94 3.1.1 AN OPTIMAL CONTROL-BASED NEWTON-TYPE METHOD 94 3.2 VARIABLE STRUCTURE ZERO FINDING METHODS 96 VII VIII CONTENTS 3.2.1 A VARIABLE STRUCTURE NEWTON METHOD TO FIND ZEROS OF A POLYNOMIAL FUNCTION 99 3.2.2 THE SPURT METHOD 107 3.3 OPTIMAL CONTROL APPROACH TO UNCONSTRAINED OPTIMIZATION PROBLEMS . 109 3.4 DIFFERENTIAL DYNAMIC PROGRAMMING APPLIED TO UNCONSTRAINED MINIMIZATION PROBLEMS 118 3.5 NOTES AND REFERENCES 124 4 NEURAL-GRADIENT DYNAMICAL SYSTEMS FOR LINEAR AND QUADRATIC PROGRAMMING PROBLEMS 127 4.1 GDSS, NEURAL NETWORKS, AND ITERATIVE METHODS 128 4.2 GDSS THAT SOLVE LINEAR SYSTEMS OF EQUATIONS 140 4.3 GDSS THAT SOLVE CONVEX PROGRAMMING PROBLEMS 146 4.3.1 STABILITY ANALYSIS OF A CLASS OF DISCONTINUOUS GDSS .... 150 4.4 GDSS THAT SOLVE LINEAR PROGRAMMING PROBLEMS 154 4.4.1 GDSS AS LINEAR PROGRAMMING SOLVERS 159 4.5 QUADRATIC PROGRAMMING AND SUPPORT VECTOR MACHINES 167 4.5.1 U-SUPPORT VECTOR CLASSIFIERS FOR NONLINEAR SEPARATION VIA GDSS 170 4.6 FURTHER APPLICATIONS: LEAST SQUARES SUPPORT VECTOR MACHINES, K-WINNERS-TAKE-ALL PROBLEM 173 4.6.1 A LEAST SQUARES SUPPORT VECTOR MACHINE IMPLEMENTED BY AGDS 173 4.6.2 A GDS THAT SOLVES THE K-WINNERS-TAKE-ALL PROBLEM .... 174 4.7 NOTES AND REFERENCES 177 5 CONTROL TOOLS IN THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND IN MATRIX PROBLEMS 179 5.1 STEPSIZE CONTROL FOR ODES 179 5.1.1 STEPSIZE CONTROL AS A LINEAR FEEDBACK SYSTEM 182 5.1.2 OPTIMAL STEPSIZE CONTROL FOR ODES 185 5.2 A FEEDBACK CONTROL PERSPECTIVE ON THE SHOOTING METHOD FOR ODES . . 191 5.2.1 A STATE SPACE REPRESENTATION OF THE SHOOTING METHOD ... 192 5.2.2 ERROR DYNAMICS OF THE ITERATIVE SHOOTING SCHEME 195 5.3 A DECENTRALIZED CONTROL PERSPECTIVE ON DIAGONAL PRECONDITIONING . . . 199 5.3.1 PERFECT DIAGONAL PRECONDITIONING 203 5.3.2 LQ PERSPECTIVE ON OPTIMAL DIAGONAL PRECONDITIONERS . . .208 5.4 CHARACTERIZATION OF MATRIX D-STABILITY USING POSITIVE REALNESS OF A FEEDBACK SYSTEM 210 5.4.1 A FEEDBACK CONTROL APPROACH TO THE D-STABILITY PROBLEM VIA STRICTLY POSITIVE REAL FUNCTIONS 213 5.4.2 D-STABILITY CONDITIONS FOR MATRICES OF ORDERS 2 AND 3 . . .216 5.5 FINDING ZEROS OF TWO POLYNOMIAL EQUATIONS IN TWO VARIABLES VIA CONTROLLABILITY AND OBSERVABILITY 218 5.6 NOTES AND REFERENCES 224 CONTENTS IX 6 EPILOGUE 227 BIBLIOGRAPHY 233 INDEX 255
adam_txt	CONTROL PERSPECTIVES ON NUMERICAL ALGORITHMS AND MATRIX PROBLEMS AMIT BHAYA EUGENIUS KASZKUREWICZ FEDERAL UNIVERSITY OF RIO DE JANEIRO RIO DE JANEIRO, BRAZIL SIAJTL SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA CONTENTS LIST OF FIGURES XI LIST OF TABLES XVII PREFACE XIX 1 BRIEF REVIEW OF CONTROL AND STABILITY THEORY 1 1.1 CONTROL THEORY BASICS 1 1.1.1 FEEDBACK CONTROL TERMINOLOGY 1 1.1.2 PID CONTROL FOR DISCRETE-TIME SYSTEMS 6 1.2 OPTIMAL CONTROL THEORY 8 1.3 LINEAR SYSTEMS, TRANSFER FUNCTIONS, REALIZATION THEORY 10 1.4 BASICS OF STABILITY OF DYNAMICAL SYSTEMS 15 1.5 VARIABLE STRUCTURE CONTROL SYSTEMS 27 1.6 GRADIENT DYNAMICAL SYSTEMS 31 1.6.1 NONSMOOTH GDSS: PERSIDSKII-TYPE RESULTS 35 1.7 NOTES AND REFERENCES 38 2 ALGORITHMS AS DYNAMICAL SYSTEMS WITH FEEDBACK 41 2.1 CONTINUOUS-TIME DYNAMICAL SYSTEMS THAT FIND ZEROS 42 2.2 ITERATIVE ZERO FINDING ALGORITHMS AS DISCRETE-TIME DYNAMICAL SYSTEMS 56 2.3 ITERATIVE METHODS FOR LINEAR SYSTEMS AS FEEDBACK CONTROL SYSTEMS . . 70 2.3.1 CLF/LOC DERIVATION OF MINIMAL RESIDUAL AND KRYLOV SUBSPACE METHODS 75 2.3.2 THE CONJUGATE GRADIENT METHOD DERIVED FROM A PROPORTIONAL-DERIVATIVE CONTROLLER 77 2.3.3 CONTINUOUS ALGORITHMS FOR FINDING OPTIMA AND THE CONTINUOUS CONJUGATE GRADIENT ALGORITHM 85 2.4 NOTES AND REFERENCES 90 3 OPTIMAL CONTROL AND VARIABLE STRUCTURE DESIGN OF ITERATIVE METHODS 93 3.1 OPTIMALLY CONTROLLED ZERO FINDING METHODS 94 3.1.1 AN OPTIMAL CONTROL-BASED NEWTON-TYPE METHOD 94 3.2 VARIABLE STRUCTURE ZERO FINDING METHODS 96 VII VIII " CONTENTS 3.2.1 A VARIABLE STRUCTURE NEWTON METHOD TO FIND ZEROS OF A POLYNOMIAL FUNCTION 99 3.2.2 THE SPURT METHOD 107 3.3 OPTIMAL CONTROL APPROACH TO UNCONSTRAINED OPTIMIZATION PROBLEMS . 109 3.4 DIFFERENTIAL DYNAMIC PROGRAMMING APPLIED TO UNCONSTRAINED MINIMIZATION PROBLEMS 118 3.5 NOTES AND REFERENCES 124 4 NEURAL-GRADIENT DYNAMICAL SYSTEMS FOR LINEAR AND QUADRATIC PROGRAMMING PROBLEMS 127 4.1 GDSS, NEURAL NETWORKS, AND ITERATIVE METHODS 128 4.2 GDSS THAT SOLVE LINEAR SYSTEMS OF EQUATIONS 140 4.3 GDSS THAT SOLVE CONVEX PROGRAMMING PROBLEMS 146 4.3.1 STABILITY ANALYSIS OF A CLASS OF DISCONTINUOUS GDSS . 150 4.4 GDSS THAT SOLVE LINEAR PROGRAMMING PROBLEMS 154 4.4.1 GDSS AS LINEAR PROGRAMMING SOLVERS 159 4.5 QUADRATIC PROGRAMMING AND SUPPORT VECTOR MACHINES 167 4.5.1 U-SUPPORT VECTOR CLASSIFIERS FOR NONLINEAR SEPARATION VIA GDSS 170 4.6 FURTHER APPLICATIONS: LEAST SQUARES SUPPORT VECTOR MACHINES, K-WINNERS-TAKE-ALL PROBLEM 173 4.6.1 A LEAST SQUARES SUPPORT VECTOR MACHINE IMPLEMENTED BY AGDS 173 4.6.2 A GDS THAT SOLVES THE K-WINNERS-TAKE-ALL PROBLEM . 174 4.7 NOTES AND REFERENCES 177 5 CONTROL TOOLS IN THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND IN MATRIX PROBLEMS 179 5.1 STEPSIZE CONTROL FOR ODES 179 5.1.1 STEPSIZE CONTROL AS A LINEAR FEEDBACK SYSTEM 182 5.1.2 OPTIMAL STEPSIZE CONTROL FOR ODES 185 5.2 A FEEDBACK CONTROL PERSPECTIVE ON THE SHOOTING METHOD FOR ODES . . 191 5.2.1 A STATE SPACE REPRESENTATION OF THE SHOOTING METHOD . 192 5.2.2 ERROR DYNAMICS OF THE ITERATIVE SHOOTING SCHEME 195 5.3 A DECENTRALIZED CONTROL PERSPECTIVE ON DIAGONAL PRECONDITIONING . . . 199 5.3.1 PERFECT DIAGONAL PRECONDITIONING 203 5.3.2 LQ PERSPECTIVE ON OPTIMAL DIAGONAL PRECONDITIONERS . . .208 5.4 CHARACTERIZATION OF MATRIX D-STABILITY USING POSITIVE REALNESS OF A FEEDBACK SYSTEM 210 5.4.1 A FEEDBACK CONTROL APPROACH TO THE D-STABILITY PROBLEM VIA STRICTLY POSITIVE REAL FUNCTIONS 213 5.4.2 D-STABILITY CONDITIONS FOR MATRICES OF ORDERS 2 AND 3 . . .216 5.5 FINDING ZEROS OF TWO POLYNOMIAL EQUATIONS IN TWO VARIABLES VIA CONTROLLABILITY AND OBSERVABILITY 218 5.6 NOTES AND REFERENCES 224 CONTENTS " IX 6 EPILOGUE 227 BIBLIOGRAPHY 233 INDEX 255
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spelling	Bhaya, Amit Verfasser (DE-588)1146241305 aut Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz Philadelphia Society for Industrial and Applied Mathematics 2006 XXV, 272 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in design and control Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Kaszkurewicz, Eugenius Verfasser (DE-588)1146241291 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014897354&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bhaya, Amit Kaszkurewicz, Eugenius Control perspectives on numerical algorithms and matrix problems Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie (DE-588)4032317-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd
subject_GND	(DE-588)4032317-1 (DE-588)4042805-9
title	Control perspectives on numerical algorithms and matrix problems
title_auth	Control perspectives on numerical algorithms and matrix problems
title_exact_search	Control perspectives on numerical algorithms and matrix problems
title_exact_search_txtP	Control perspectives on numerical algorithms and matrix problems
title_full	Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz
title_fullStr	Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz
title_full_unstemmed	Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz
title_short	Control perspectives on numerical algorithms and matrix problems
title_sort	control perspectives on numerical algorithms and matrix problems
topic	Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie (DE-588)4032317-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd
topic_facet	Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie Numerische Mathematik
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