Title :
Optimisation of real functions of complex matrices for the adaptive estimation of complex sources
Author :
Javidi, Soroush ; Mandic, Danilo P. ; Kuh, Anthony
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll., London, UK
Abstract :
The second order Taylor series expansion (TSE) of scalar functions of complex matrices is explored in order to provide a new tool for gradient-based optimisation in the complex domain. The expansion is provided both in the augmented real and complex matrix spaces, as well as the multidimensional complex domain. The duality (isomorphism) between the augmented spaces is established and consequently the relation of the first- and second-order terms (gradient and Hessian) of the TSE in these spaces are introduced. Finally, a study of the trade-off between performance and computational complexity of algorithms for the estimation of complex sources in the two augmented spaces is performed.
Keywords :
Hessian matrices; adaptive estimation; augmented reality; multidimensional signal processing; optimisation; Taylor series expansion; adaptive estimation; augmented real matrix; complex matrices; gradient-based optimisation; multidimensional complex domain; real function optimisation; scalar function; Adaptive estimation; Adaptive filters; Adaptive signal processing; Algorithm design and analysis; Calculus; Signal analysis; Signal processing algorithms; Statistical analysis; Taylor series; Zirconium; Complex matrix calculus; Newton optimisation; augmented complex matrix space; complex eigenvalues;
Conference_Titel :
Green Circuits and Systems (ICGCS), 2010 International Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4244-6876-8
Electronic_ISBN :
978-1-4244-6877-5
DOI :
10.1109/ICGCS.2010.5543101