Markovsky I. Low Rank Approximation. Algorithms, Implementation, Applications

Springer, 2012. — 260.Data Approximation by Low-complexity Models details 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. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal 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.Part I Linear Modeling Problems
From Data to Models
Algorithms
Applications in System, Control, and Signal Processing
Part II Miscellaneous Generalizations
Missing Data, Centering, and
Nonlinear Static Data Modeling
Fast Measurements of Slow Processes
A: Approximate Solution of an Overdetermined System of Equations
B: Proofs
P: Problems