Low Rank Approximation: Algorithms, Implementation, Applications.
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications 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. 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 modeling, and array processing;
- machine learning: multidimensional scaling and recommender system;
- computer vision: algebraic curve fitting and fundamental matrix estimation;
- bioinformatics for microarray data analysis;
- chemometrics for multivariate calibration;
- psychometrics for factor analysis; and
- computer algebra for approximate common divisor computation.