Quadratic optimization for simultaneous matrix diagonalization

• Published in: IEEE transactions on signal processing Vol. 54; no. 9; pp. 3270 - 3278
• Main Authors: Vollgraf, R., Obermayer, K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Blind source separation; Blind source separation (BSS); Constrictions; Coordinate measuring machines; Detection, estimation, filtering, equalization, prediction; Eigenvalues and eigenfunctions; Exact sciences and technology; Information, signal and communications theory; Jacobian matrices; joint diagonalization; Mathematical analysis; Matrices; Matrix methods; Miscellaneous; Optimization; Optimization algorithms; Principal component analysis; quadratic optimization; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; Source separation; Statistics; Studies; Symmetric matrices; Telecommunications and information theory; Tensile stress; Transformations; Matrix diagonalization; Second order; Hermite interpolation; Blind source separation; Blind source separation (BSS); quadratic optimization; Implementation; Optimization; Orthogonal transformation; Least squares method; Signal processing; joint diagonalization; Objective function; Fast algorithm

Simultaneous diagonalization of a set of matrices is a technique that has numerous applications in statistical signal processing and multivariate statistics. Although objective functions in a least-squares sense can be easily formulated, their minimization is not trivial, because constraints and fou...