Approximate Matrix and Tensor Diagonalization by Unitary Transformations: Convergence of Jacobi-Type Algorithms

DOI10.1137/19M125950XzbMath1453.90168arXiv1905.12295OpenAlexW3041284015MaRDI QIDQ5131963

Pierre Comon, Konstantin Usevich, Jian Ze Li

Publication date: 9 November 2020

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.12295

zbMATH Keywords

unitary grouplocal convergenceGivens rotationsoptimization on manifoldsŁojasiewicz gradient inequalityapproximate tensor diagonalization

Mathematics Subject Classification ID

Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Complexity and performance of numerical algorithms (65Y20) Multilinear algebra, tensor calculus (15A69) Local Riemannian geometry (53B20) Methods of local Riemannian geometry (53B21)

Related Items (8)

Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations ⋮ Jacobi-type algorithms for homogeneous polynomial optimization on Stiefel manifolds with applications to tensor approximations ⋮ Alternating Mahalanobis Distance Minimization for Accurate and Well-Conditioned CP Decomposition ⋮ Convergence of Gradient-Based Block Coordinate Descent Algorithms for Nonorthogonal Joint Approximate Diagonalization of Matrices ⋮ Projectively and Weakly Simultaneously Diagonalizable Matrices and their Applications ⋮ Trace maximization algorithm for the approximate tensor diagonalization ⋮ A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors ⋮ Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization

Uses Software

• Manopt

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