This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: . variable projection for structured low-rank approximation;. missing data estimation;. data-driven filtering and control;. stochastic model representation and identification;. identification of polynomial time-invariant systems; and. blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. "Each chapter is completed with a new section of exercises to which complete solutions are provided." Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

Autorentext

Ivan Markovsky obtained Ph.D. in Electrical Engineering from the Katholieke Universiteit Leuven in 2005. Since then, he is teaching and doing research in control and system theory at the School of Electronics and Computer Science (ECS) of the University of Southampton and the Department of Fundamental Electricity and Instrumentation (ELEC) of the Vrije Universiteit Brussel, where he is currently an associate processor. His research interests are structured low-rank approximation, system identification, and data-driven control, topics on which he has published 70 peer-reviewed papers, 7 book chapters, and 2 monographs. He is an associate editor of the International Journal of Control and the SIAM Journal of Matrix Analysis and Applications. In 2011, Ivan Markovsky was awarded an ERC starting grant on the topic of structured low-rank approximation.

Zusammenfassung

Matrix low-rank approximation is intimately related to data modelling by a linear system; a problem that arises frequently in many different fields. This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include:

• system and control theory: approximate realization, model reduction, output error and errors-in-variables identification;

• signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modelling, and array processing;

• computer algebra for approximate factorization and common divisor computation;

• computer vision for image deblurring and segmentation;

• machine learning for information retrieval and clustering;

• bioinformatics for microarray data analysis;

• chemometrics for multivariate calibration; and

• psychometrics for factor analysis.

Special knowledge from the respective application fields is not required. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB® examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis.

Data Approximation by Low-complexity Models is a broad survey of the theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary electronic lecture slides, problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

Inhalt

Chapter 1. Introduction.- Part I: Linear modeling problems.- Chapter 2. From data to models.- Chapter 3. Exact modelling.- Chapter 4. Approximate modelling.- Part II: Applications and generalizations.- Chapter 5. Applications.- Chapter 6. Data-driven ltering and control.- Chapter 7. Nonlinear modeling problems.- Chapter 8. Dealing with prior knowledge.- Index.