A new convergence proof for the higher-order power method and generalizations

2014/07/17 by André Uschmajew, Uschmajew, André · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1407.4586

openalex publication_date 2014/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results from the theory of Łojasiewicz inequalities to the equivalent, unconstrained alternating least squares algorithm for best rank-one tensor approximation.

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• Multi-subspace power method for decomposing partially symmetric tensors

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