Approximate matrix and tensor diagonalization by unitary transformations: convergence of Jacobi-type algorithms

Autor: Konstantin Usevich, Pierre Comon, Jianze Li
Přispěvatelé: Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong (SRIBD), GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes (GIPSA-GAIA), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), ANR-19-CE23-0021,LeaFleT,Apprentissage des réseaux de neurones avec des fonctions d'activation flexibles par les méthodes tensorielles(2019), European Project: 320594,EC:FP7:ERC,ERC-2012-ADG_20120216,DECODA(2013), European Project: 11601371, GIPSA - Communication Information and Complex Systems (GIPSA-CICS [2010-2015]), Département Images et Signal (GIPSA-DIS [2007-2015]), Grenoble Images Parole Signal Automatique (GIPSA-lab [2007-2015]), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab [2007-2015]), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS), PNRIA, ANR-19-CE23-0021,LeaFleT,LEArning neural networks with FLExible nonlinearities by Tensor methods
Jazyk: angličtina
Rok vydání: 2020
Předmět:
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
Unitary state
Theoretical Computer Science
symbols.namesake
Matrix (mathematics)
Unitary group
Convergence (routing)
unitary group
FOS: Mathematics
0202 electrical engineering
electronic engineering
information engineering
Mathematics - Numerical Analysis
Tensor
0101 mathematics
Mathematics - Optimization and Control
Mathematics
90C30
53B21
53B20
15A69
65K10
65Y20
Weak convergence
Lojasiewicz gradient inequality
020206 networking & telecommunications
Numerical Analysis (math.NA)
Givens rotations
optimization on manifolds
Local convergence
Jacobi eigenvalue algorithm
Optimization and Control (math.OC)
symbols
local convergence
approximate tensor diagonalization
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Algorithm
Software
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: SIAM Journal on Optimization
SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2020, 30 (4), pp.2998-3028. ⟨10.1137/19M125950X⟩
SIAM Journal on Optimization, 2020, 30 (4), pp.2998-3028. ⟨10.1137/19M125950X⟩
ISSN: 1052-6234
DOI: 10.1137/19M125950X⟩
Popis: International audience; We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence results, and prove local linear convergence of this algorithm. The convergence results also apply to the case of real-valued tensors.
Databáze: OpenAIRE
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