Preface	5
	Contents	7
	List of Contributors	9
	Part I Basic Concepts	13
	Introduction to Model Order Reduction	14
	1 Introduction	14
	2 Transfer Function, Stability and Passivity	23
	3 A Short Account of Techniques for Model Order Reduction	29
	References	42
	Linear Systems, Eigenvalues, and Projection	44
	1 Introduction	44
	2 Linear Systems	48
	3 Subspace Methods	49
	References	55
	Part II Theory	58
	Structure-Preserving Model Order Reduction of RCL Circuit Equations	60
	1 Introduction	60
	2 Formulation of General RCL Circuits as Integro-DAEs	62
	3 Structure-Preserving Model Order Reduction	65
	4 Equivalent First-Order Form of Integro-DAEs	68
	5 Krylov-Subspace Projection and PRIMA	72
	6 The SPRIM Algorithm	74
	7 Pade-Type Approximation Property of SPRIM	77
	8 Numerical Examples	78
	9 Concluding Remarks	81
	Acknowledgement	82
	References	82
	A Unified Krylov Projection Framework for Structure- Preserving Model Reduction	86
	1 Introduction	86
	2 A unified Krylov Projection Structure-Preserving Model Order Reduction Framework	87
	3 Structure of Krylov Subspace and Arnoldi Process	93
	4 RCL and RCS Systems	94
	References	103
	Model Reduction via Proper Orthogonal Decomposition	106
	1 Introduction	106
	2 Proper Orthogonal Decomposition	107
	3 POD in Radiative Heat Transfer	113
	4 Conclusions and Future Perspectives	116
	Acknowledgments	118
	References	118
	PMTBR: A Family of Approximate Principal- components- like Reduction Algorithms	122
	1 Introduction	122
	2 Basic Algorithm	124
	3 Algorithmic Variants	128
	4 Analysis and Comparisons	134
	5 Experimental Results	136
	6 Conclusions	141
	References	142
	A Survey on Model Reduction of Coupled Systems.	144
	1 Introduction	144
	2 Coupled Systems	145
	3 Model Reduction Approaches for Coupled Systems	148
	4 Numerical Examples	157
	References	164
	Space Mapping and Defect Correction	168
	1 Introduction	168
	2 Fine and Coarse Models in Optimization	169
	3 Space-Mapping Optimization	171
	4 Defect Correction and Space Mapping	175
	5 Manifold Mapping, the Improved Space Mapping Algorithm	178
	6 Examples	181
	7 Conclusions	186
	References	186
	Modal Approximation and Computation of Dominant Poles	188
	1 Introduction	188
	2 Transfer Functions, Dominant Poles and Modal Equivalents	188
	3 Computing Dominant Poles	190
	4 Generalizations	197
	5 Numerical Examples	199
	6 Conclusions	203
	Acknowledgement	203
	References	203
	Some Preconditioning Techniques for Saddle Point Problems	206
	1 Introduction	206
	2 Properties of Saddle Point Systems	207
	3 Preconditioned Krylov Subspace Methods	208
	4 Block Preconditioners	210
	5 Augmented Lagrangian Formulations	212
	6 Constraint Preconditioning	213
	7 Other Techniques	216
	8 Numerical Examples	217
	9 Conclusions	219
	References	220
	Time Variant Balancing and Nonlinear Balanced Realizations	224
	1 Introduction	224
	2 Time Varying Linear Systems	225
	3 Sliding Interval Balancing	230
	4 Nonlinear Balancing	235
	5 Global Balancing	250
	6 Mayer-Lie Interpolation	253
	7 Nonlinear Model Reduction	255
	8 How Far Can You Go?	256
	9 Conclusions	258
	References	259
	Singular Value Analysis and Balanced Realizations for Nonlinear Systems	262
	1 Introduction	262
	2 Singular Value Analysis of Nonlinear Operators	263
	3 Balanced Realization for Linear Systems	266
	4 Basics of Nonlinear Balanced Realizations	269
	5 Balanced Realizations Based on Singular Value Analysis of Hankel Operators	273
	6 Model Order Reduction	276
	7 Numerical Example	278
	8 Conclusion	282
	References	282
	Part III Research Aspects and Applications	284
	Matrix Functions	286
	1 Introduction	286
	2 Matrix Functions	286
	3 Computational Aspects	289
	4 The Exponential Function	296
	5 The Matrix Sign Function	304
	References	311
	Model Reduction of Interconnected Systems	316
	1 Introduction	316
	2 Interconnected Systems Balanced Truncation	319
	3 Krylov Techniques for Interconnected Systems	323
	4 Examples of Structured Model Reduction Problems	327
	5 Concluding Remarks	330
	Acknowledgment	331
	References	331
	Quadratic Inverse Eigenvalue Problem and Its Applications to Model Updating — An Overview	334
	1 Introduction	334
	2 Challenges	336
	3 Quadratic Inverse Eigenvalue Problem	338
	4 Spill-Over Phenomenon	347
	5 Least Squares Update	349
	6 Conclusions	350
	References	350
	Data-Driven Model Order Reduction Using Orthonormal Vector Fitting	352
	1 Identi.cation Problem	353
	2 Vector Fitting	355
	3 Orthonormal Vector Fitting	358
	4 Example	362
	5 Conclusion	364
	6 Acknowledgements	364
	A Sanathanan-Koerner Iteration	364
	B Real-Valued State Space	366
	References	368
	Model-Order Reduction of High-Speed Interconnects Using Integrated Congruence Transform	372
	1 High-Speed Interconnects and Its Effects on Signal Propagation	372
	2 Time-Domain Macromodeling of High-Speed Interconnects	375
	3 Time-Domain Macromodeling Through MOR	383
	4 Numerical Computations	404
	5 Conclusion	410
	References	410
	Model Order Reduction for MEMS: Methodology and Computational Environment for Electro- Thermal Models	414
	1 Introduction	414
	2 Applications	415
	3 Model Order Reduction: Method and Numerical Results	416
	4 Computational Environment	418
	5 Error Estimation	420
	6 Coupling of the Reduced Models	421
	7 Model Order Reduction as a Fast Solver	423
	8 Advanced Development	425
	9 Summary	427
	References	427
	Model Order Reduction of Large RC Circuits	432
	1 Introduction	432
	2 Gaussian Elimination Background	433
	3 RC-in RC-out Reduction	439
	4 Elimination for Synthesis	446
	5 Computational Aspects	451
	6 Conclusion	455
	References	456
	Reduced Order Models of On-Chip Passive Components and Interconnects, Workbench and Test Structures	458
	1 Extraction of the EM-FW State Models for Passive Components	458
	2 Finite States Representation by Finite Integrals Technique	461
	3 State Representation of the Boundary Conditions	465
	4 ROMWorkBench	468
	5 All Levels Reduced Order Modelling	470
	6 Test Structures	471
	7 Conclusions	476
	Acknowledgment	478
	References	478
	Index	480