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© Copyright I.W.M. Bleylevens, Maastricht 2010 Cover design: D&L Graphics, Kerkrade Printing: Schrijen-Lippertz, Voerendaal ISBN: 978-90-8590-046-7 All rights reserved. No part of this thesis may be reproduced, stored in a retrieval system of any nature, or transmitted in any form by any means, electronic, mechanical, photocopying, recording or otherwise, included a complete or partial transcription, without the permission of the author.
ALGEBRAIC POLYNOMIAL SYSTEM SOLVING AND APPLICATIONS PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Maastricht, op gezag van de Rector Magnificus, Prof. mr. G.P.M.F. Mols, volgens het besluit van het College van Decanen, in het openbaar te verdedigen op donderdag 9 december 2010 om 12.00 uur door Ivo Werner Maria Bleylevens.
Page 3 and 4: Stellingen behorende bij het proefs
Page 5: ALGEBRAIC POLYNOMIAL SYSTEM SOLVING
Page 9: For all those I love...
Page 12 and 13: ii CONTENTS II Global Optimization
Page 14 and 15: iv CONTENTS 12.2 Directions for fur
Page 17 and 18: Chapter 1 Introduction 1.1 Motivati
Page 19 and 20: 1.3. RESEARCH QUESTIONS 5 The goal
Page 21 and 22: 1.4. THESIS OUTLINE 7 Jacobi-Davids
Page 23: Part I General introduction and bac
Page 26 and 27: 12 CHAPTER 2. ALGEBRAIC BACKGROUND
Page 39 and 40: Chapter 3 Solving polynomial system
Page 41 and 42: 3.1. SOLVING POLYNOMIAL EQUATIONS I
Page 43 and 44: 3.2. METHODS FOR SOLVING POLYNOMIAL
Page 49 and 50: 3.3. THE STETTER-MÖLLER MATRIX MET
Page 51 and 52: 3.5. EXAMPLE 37 applying the Stette
Page 53: 3.5. EXAMPLE 39 be: I = 〈13x 2 2
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Chapter 4 Global optimization of mu
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4.1. THE GLOBAL MINIMUM OF A DOMINA
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4.3. AN EXAMPLE 47 Using the matric
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4.3. AN EXAMPLE 49 the Stetter-Möl
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Chapter 5 An nD-systems approach in
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5.1. THE ND-SYSTEM 53 cerned with t
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5.1. THE ND-SYSTEM 55 Example 5.1.
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5.1. THE ND-SYSTEM 57 Figure 5.2: T
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5.3. EFFICIENCY OF THE ND-SYSTEMS A
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Chapter 6 Iterative eigenvalue solv
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6.2. THE JACOBI-DAVIDSON METHOD 83
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6.2. THE JACOBI-DAVIDSON METHOD 85
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6.4. PROJECTION TO STETTER-STRUCTUR
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6.5. A JACOBI-DAVIDSON METHOD FOR C
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6.5. A JACOBI-DAVIDSON METHOD FOR C
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108 CHAPTER 7. NUMERICAL EXPERIMENT
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Part III H 2 Model-order Reduction
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136 CHAPTER 8. H 2 MODEL-ORDER REDU
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Chapter 10 H 2 Model-order reductio
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10.1. SOLVING THE SYSTEM OF QUADRAT
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10.1. SOLVING THE SYSTEM OF QUADRAT
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10.2. LINEARIZING A POLYNOMIAL EIGE
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10.3. THE KRONECKER CANONICAL FORM
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10.4. COMPUTING THE APPROXIMATION G
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10.6. EXAMPLES 181 5. Compute the n
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10.6. EXAMPLES 183 Figure 10.1: Spa
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10.6. EXAMPLES 185 Figure 10.3: The
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10.6. EXAMPLES 187 Figure 10.5: Imp
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10.6. EXAMPLES 189 Figure 10.7: Str
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10.6. EXAMPLES 191 Figure 10.8: Pol
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10.6. EXAMPLES 193 Table 10.1: Redu
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Chapter 11 H 2 Model-order reductio
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11.2. LINEARIZING THE TWO-PARAMETER
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11.3. KRONECKER CANONICAL FORM OF A
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11.4. COMPUTING THE APPROXIMATION G
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11.5. EXAMPLE 223 AãN−2 (ρ 1 ,
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11.5. EXAMPLE 225 of both matrices
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11.5. EXAMPLE 227 of solutions (ρ
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Chapter 12 Conclusions & directions
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12.1. CONCLUSIONS 231 used first. T
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12.1. CONCLUSIONS 233 solver as des
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12.2. DIRECTIONS FOR FURTHER RESEAR
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Bibliography [1] W. Adams and P. Lo
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BIBLIOGRAPHY 239 [26] A. Cayley. On
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BIBLIOGRAPHY 241 [58] M.E. Hochsten
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BIBLIOGRAPHY 243 [90] S. Prajna, A.
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Appendix A A linearization techniqu
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A.2. LINEARIZATION WITH RESPECT TO
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A.3. EXAMPLE 251 The first step of
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A.3. EXAMPLE 253 where the eigenvec
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256 APPENDIX B. POLYNOMIAL TEST SET
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258 SUMMARY vector. This routine is
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260 SUMMARY globally optimal approx
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262 SAMENVATTING De matrix-vrije im
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264 SAMENVATTING eigenwaarde proble
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List of Publications [1] I.W.M. Ble
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List of Symbols and Abbreviations A
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LIST OF FIGURES 271 7.7 Residual no
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Index H 2 model-order reduction pro
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