UID:
almahu_9947366315402882
Format:
1 online resource (266 p.)
ISBN:
1-282-28872-5
,
9786612288722
,
0-08-095572-X
Series Statement:
Mathematics in science and engineering ; 62
Content:
Algorithms, graphs, and computers
Note:
Description based upon print version of record.
,
Front Cover; Algorithms Graphs and Computers; Copyright Page; Contents; Preface; Chapter One. COMMUTING AND COMPUTING; 1. Introduction; 2. A Commuting Problem; 3. Enumeration of Paths; 4. Tree Diagrams; 5. Timing and the Shortest Route; 6. An Improved Map; 7. The Array of Times; 8. Arbitrary Starting Point; 9. Minimum Time Functions; 10. The Minimum Function; 11. Equations for the fi; 12. Reduced Tree; 13. General Map; 14. Solving the Equations; 15. Why Not Enumeration Using Computers?; 16. Graphs; 17. The Problem of the Königsberg Bridges; 18. Systems and States; 19. Critical Path Analysis
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20. Summing UpBibliography and Comments; Chapter Two. THE METHOD OF SUCCESSIVE APPROXIMATIONS; 1. Introduction; 2. A Simple Example of Successive Approximations; 3. A Simple Example of the Failure of the Method; 4. Algorithms; 5. Computer Programming; 6. Algorithms for Solving x = f(x); 7. The Newton-Raphson Method: Square Roots; 8. An Example; 9. Enter the Digital Computer; 10. Stop Rules; 11. Flow Charts for the Determination of S a; 12. What Initial Approximation?; 13. An Approximation Method of Steinhaus; 14. Successive Approximations for a Simple Routing Problem
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15. The Map of Fig. 3 of Chapter One16. Determination of Optimal Policy; 17. A Different Initial Policy; 18. Successive Approximations for a General Map; 19. Computer Program; 20. The Connection Matrix and A Second Programming Method; 21. Fictitious Links; 22. Paths With a Given Number of Junctions; 23. A Labelling Algorithm; 24. Working Back From the End; Miscellaneous Exercises; Bibliography and Comment; Chapter Three. FROM CHICAGO TO THE GRAND CANYON BY CAR AND COMPUTER : Difficulties Associated With Large Maps; 1. Introduction; 2. How to Plan a Vacation
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3. A Particular Initial Approximation4. The Peculiarities of Structure; 5. Computer Program; 6. Storage Considerations; 7. Use of Tapes; 8. Storage of Sparse Data; 9. Calculation of the tij; 10. Transformation of Systems; 11. Stratification; 12. Acceleration of Convergence; 13. Design of Electric Power Stations; Miscellaneous Exercises; Bibliography and Comments; Chapter Four. PROOF OF THE VALIDITY OF THE METHOD; 1. Will the Method Always Work?; 2. Is There at Least One Solution?; 3. How Do We Find the Desired Solution?; 4. Monotonicity; 5. The Upper Solution; 6. The Lower Solution
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7. Experimental Proof of Uniqueness8. Uniqueness of Solution; 9. Determination of Optimal Policy; 10. Arbitrary Initial Approximation; 11. Least Time to Move k Steps; 12. Number of Iterations; Miscellaneous Exercises; Bibliography and Comment; Chapter Five. JUGGLING JUGS; 1. A Classical Puzzle; 2. Precise Formulation; 3. Trial and Error; 4. Tree Diagrams; 5. Some Further Observations; 6. Enumeration by Computer; 7. A Geometrical Representation; 8. Cost Matrix; 9. Connection Matrix; 10. Minimum Cost Functions; 11. Powers of the Adjacency Matrix; 12. Functional Equations
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13. Successive Approximations
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English
Additional Edition:
ISBN 0-12-084840-6
Language:
English
