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List of Publications [1] I.W.M. Bleylevens, M.E. Hochstenbach, and R.L.M. Peeters. Polynomial optimization and a Jacobi–Davidson type method for commuting matrices. Submitted, 2010. [2] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. A generalized eigenvalue approach to H 2 model-order reduction. Proceedings of the 27th Benelux Meeting on Systems and Control, Heeze, 2008. [3] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. Efficiency improvement in an nD-systems approach to polynomial optimization. Journal of Symbolic Computation, 42(1–2): 30–53, 2007. [4] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. Optimal H 2 model reduction from order N to N − 2. Internal Report M07-01, Department of Mathematics, Maastricht University, 2007. [5] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. Optimal H 2 model reduction from order N to N − 2. Proceedings of the 13th ILAS Conference, Amsterdam, 2006. [6] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. An nD-systems approach to global polynomial optimization with an application to H 2 model-order reduction. Proceedings of the 44th IEEE CDC and the ECC, Seville, Spain, 2005. [7] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. Efficiency improvement in an nD-systems approach to polynomial optimization. Proceedings of the MEGA 2005: Effective Methods in Algebraic Geometry Computing in and with algebraic geometry: Theory, Algorithms, Implementations, Applications, Alghero, Sardinia, Italy, 2005. [8] I.W.M. Bleylevens, R.L.M. Peeters, and B. Hanzon. Efficient polynomial optimization with an nD-systems approach. Proceedings of the 24th Benelux Meeting on Systems and Control, Houffalize, Belgium, 2005. 267
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Stellingen behorende bij het proefs
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ALGEBRAIC POLYNOMIAL SYSTEM SOLVING
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ALGEBRAIC POLYNOMIAL SYSTEM SOLVING
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For all those I love...
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ii CONTENTS II Global Optimization
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iv CONTENTS 12.2 Directions for fur
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Chapter 1 Introduction 1.1 Motivati
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1.3. RESEARCH QUESTIONS 5 The goal
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1.4. THESIS OUTLINE 7 Jacobi-Davids
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Part I General introduction and bac
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12 CHAPTER 2. ALGEBRAIC BACKGROUND
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Chapter 3 Solving polynomial system
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3.1. SOLVING POLYNOMIAL EQUATIONS I
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3.2. METHODS FOR SOLVING POLYNOMIAL
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3.3. THE STETTER-MÖLLER MATRIX MET
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3.5. EXAMPLE 37 applying the Stette
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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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Page 251 and 252: Bibliography [1] W. Adams and P. Lo
Page 253 and 254: BIBLIOGRAPHY 239 [26] A. Cayley. On
Page 255 and 256: BIBLIOGRAPHY 241 [58] M.E. Hochsten
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Page 265 and 266: A.3. EXAMPLE 251 The first step of
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Page 270 and 271: 256 APPENDIX B. POLYNOMIAL TEST SET
Page 272 and 273: 258 SUMMARY vector. This routine is
Page 274 and 275: 260 SUMMARY globally optimal approx
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Page 278 and 279: 264 SAMENVATTING eigenwaarde proble
Page 282 and 283: 268 LIST OF PUBLICATIONS [9] I.W.M.
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Page 286 and 287: List of Tables 2.1 Monomial orderin
Page 288: 274 INDEX Lagrange Multiplier, 100
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