Naslov
Efficient Algorithms for Joint Approximate Diagonalization of Multiple Matrices

Autori
Bosner, Nela

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, prošireni sažetak, znanstveni

Skup
The International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC'22)

Mjesto i datum
Porto, Portugal, 27.06.2022. - 29.06.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Recenziran

Ključne riječi
joint approximate diagonalization ; constrained optimization ; conjugate gradient method ; matrix manifolds.

Sažetak
Joint approximate diagonalization (JAD) of multiple matrices is a core problem in many applications, such as: blind source separation, parameter identification in exponential sum, canonical polyadic decomposition of a tensor used in chemometrics, telecommunications, psychometrics, data mining, machine learning, ... In this work we propose two numerical methods for computing JAD, based on constrained optimization on two different matrix manifolds, with emphasis on their numerical properties and efficiency. Following numerical analysis, we introduce modifications and parallel implementation of the proposed methods that increase their efficiency. Numerical experiments prove that these modifications speed-up execution time of the proposed methods by factor 3 -- 4 per iteration, for large number of matrices.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA