Systems Analysis by Graphs and Matroids : Structural Solvability and Controllability / by Kazuo Murota
(Algorithms and Combinatorics, Study and Research Texts ; 3)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg , 1987 |
| 本文言語 | 英語 |
| 大きさ | X, 284 p : online resource |
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| 内容注記 | 1. Preliminaries 1. Convention and Notation 2. Algebra 3. Graph 4. Matroid 2. Graph-Theoretic Approach to the Solvability of a System of Equations 5. Structural Solvability of a System of Equations 6. Representation Graph 7. Graphical Conditions for Structural Solvability 8. Decompositions of a Graph by Menger-type Linkings 9. Decompositions and Reductions of a System of Equations 10. Application of the Graphical Technique 11. Examples 3. Graph-Theoretic Approach to the Controllability of a Dynamical System 12. Descriptions of a Dynamical System 13. Controllability of a Dynamical System 14. Graphical Conditions for Structural Controllability 15. Discussions 4. Physical Observations for Faithful Formulations 16. Mixed Matrix for Modeling Two Kinds of Numbers 17. Algebraic Implication of Dimensional Consistency 18. Physical Matrix 5 Matroid-Theoretic Approach to the Solvability of a System of Equations 19. Rank of a Mixed Matrix 20. Algorithm for Computing the Rank of a Mixed Matrix 21. Matroidal Conditions for Structural Solvability 22. Combinatorial Canonical Form of a Layered Mixed Matrix 23. Relation to Other Decompositions 24. Block-Triangularization of a Mixed Matrix 25. Decomposition of a System of Equations 26. Miscellaneous Notes 6. Matroid-Theoretic Approach to the Controllability of a Dynamical System 27. Dynamical Degree of a Dynamical System 28. Matroidal Conditions for Structural Controllability 29. Algorithm for Testing the Structural Controllability 30. Examples 31. Discussions Conclusion References |
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| 一般注記 | Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers |
| 著者標目 | *Murota, Kazuo author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Combinatorics FREE:Mathematics FREE:Combinatorics |
| 分 類 | DC23:511.6 |
| 巻冊次 | ISBN:9783642615863 
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| ISBN | 9783642615863 |
| URL | http://dx.doi.org/10.1007/978-3-642-61586-3 |
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