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06108nmm a22003855i 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20230705150624.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
121227s1994 xxk| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781447134671 |
| -- |
978-1-4471-3467-1 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
629.8312 |
| Edition number |
23 |
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| Classification number |
003 |
| Edition number |
23 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Helmke, Uwe. |
| 9 (RLIN) |
19733 |
| 245 ## - TITLE STATEMENT |
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| Title |
Optimization and Dynamical Systems |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Uwe Helmke, John B. Moore. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st ed. 1994. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
London : |
| Name of publisher, distributor, etc. |
Springer London : |
| -- |
Imprint: Springer, |
| Date of publication, distribution, etc. |
1994. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XIII, 403 p. 2 illus. |
| Other physical details |
online resource. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1 Matrix Eigenvalue Methods -- 1.1 Introduction -- 1.2 Power Method for Diagonalization -- 1.3 The Rayleigh Quotient Gradient Flow -- 1.4 The QR Algorithm -- 1.5 Singular Value Decomposition (SVD) -- 1.6 Standard Least Squares Gradient Flows -- 2 Double Bracket Isospectral Flows -- 2.1 Double Bracket Flows for Diagonalization -- 2.2 Toda Flows and the Riccati Equation -- 2.3 Recursive Lie-Bracket Based Diagonalization -- 3 Singular Value Decomposition -- 3.1 SVD via Double Bracket Flows -- 3.2 A Gradient Flow Approach to SVD -- 4 Linear Programming -- 4.1 The Rôle of Double Bracket Flows -- 4.2 Interior Point Flows on a Polytope -- 4.3 Recursive Linear Programming/Sorting -- 5 Approximation and Control -- 5.1 Approximations by Lower Rank Matrices -- 5.2 The Polar Decomposition -- 5.3 Output Feedback Control -- 6 Balanced Matrix Factorizations -- 6.1 Introduction -- 6.2 Kempf-Ness Theorem -- 6.3 Global Analysis of Cost Functions -- 6.4 Flows for Balancing Transformations -- 6.5 Flows on the Factors X and Y -- 6.6 Recursive Balancing Matrix Factorizations -- 7 Invariant Theory and System Balancing -- 7.1 Introduction -- 7.2 Plurisubharmonic Functions -- 7.3 The Azad-Loeb Theorem -- 7.4 Application to Balancing -- 7.5 Euclidean Norm Balancing -- 8 Balancing via Gradient Flows -- 8.1 Introduction -- 8.2 Flows on Positive Definite Matrices -- 8.3 Flows for Balancing Transformations -- 8.4 Balancing via Isodynamical Flows -- 8.5 Euclidean Norm Optimal Realizations -- 9 Sensitivity Optimization -- 9.1 A Sensitivity Minimizing Gradient Flow -- 9.2 Related L2-Sensitivity Minimization Flows -- 9.3 Recursive L2-Sensitivity Balancing -- 9.4 L2-Sensitivity Model Reduction -- 9.5 Sensitivity Minimization with Constraints -- A Linear Algebra -- A.1 Matrices and Vectors -- A.2 Addition and Multiplication of Matrices -- A.3 Determinant and Rank of a Matrix -- A.4 Range Space, Kernel and Inverses -- A.5 Powers, Polynomials, Exponentials and Logarithms -- A.6 Eigenvalues, Eigenvectors and Trace -- A.7 Similar Matrices -- A.8 Positive Definite Matrices and Matrix Decompositions -- A.9 Norms of Vectors and Matrices -- A.10 Kronecker Product and Vec -- A.11 Differentiation and Integration -- A.12 Lemma of Lyapunov -- A.13 Vector Spaces and Subspaces -- A.14 Basis and Dimension -- A.15 Mappings and Linear Mappings -- A.16 Inner Products -- B Dynamical Systems -- B.1 Linear Dynamical Systems -- B.2 Linear Dynamical System Matrix Equations -- B.3 Controllability and Stabilizability -- B.4 Observability and Detectability -- B.5 Minimality -- B.6 Markov Parameters and Hankel Matrix -- B.7 Balanced Realizations -- B.8 Vector Fields and Flows -- B.9 Stability Concepts -- B.10 Lyapunov Stability -- C Global Analysis -- C.1 Point Set Topology -- C.2 Advanced Calculus -- C.3 Smooth Manifolds -- C.4 Spheres, Projective Spaces and Grassmannians -- C.5 Tangent Spaces and Tangent Maps -- C.6 Submanifolds -- C.7 Groups, Lie Groups and Lie Algebras -- C.8 Homogeneous Spaces -- C.9 Tangent Bundle -- C.10 Riemannian Metrics and Gradient Flows -- C.11 Stable Manifolds -- C.12 Convergence of Gradient Flows -- References -- Author Index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Control engineering. |
| 9 (RLIN) |
19734 |
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| Topical term or geographic name entry element |
Dynamical systems. |
| 9 (RLIN) |
19735 |
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| Topical term or geographic name entry element |
Mathematical models. |
| 9 (RLIN) |
19736 |
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| Topical term or geographic name entry element |
Telecommunication. |
| 9 (RLIN) |
19737 |
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| Topical term or geographic name entry element |
System theory. |
| 9 (RLIN) |
19738 |
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| Topical term or geographic name entry element |
Control theory. |
| 9 (RLIN) |
19739 |
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| Topical term or geographic name entry element |
Mathematical optimization. |
| 9 (RLIN) |
19740 |
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| Topical term or geographic name entry element |
Calculus of variations. |
| 9 (RLIN) |
19741 |
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| Topical term or geographic name entry element |
Control and Systems Theory. |
| 9 (RLIN) |
19742 |
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| Topical term or geographic name entry element |
Dynamical Systems. |
| 9 (RLIN) |
19743 |
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| Topical term or geographic name entry element |
Mathematical Modeling and Industrial Mathematics. |
| 9 (RLIN) |
19744 |
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| Topical term or geographic name entry element |
Communications Engineering, Networks. |
| 9 (RLIN) |
19745 |
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| Topical term or geographic name entry element |
Systems Theory, Control . |
| 9 (RLIN) |
19746 |
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| Topical term or geographic name entry element |
Calculus of Variations and Optimization. |
| 9 (RLIN) |
19747 |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Moore, John B. |
| Relator term |
author. |
| Relationship |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) |
19748 |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-1-4471-3467-1">https://doi.org/10.1007/978-1-4471-3467-1</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
e-Book |
