Accelerating the Computation of Tensor Z-eigenvalues

2023/07/21 by Sara Pollock, Pollock, Sara, R. N. Shroff +1 · 2 citations
Computer Science · Mathematics · #15A18 #15A69 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Parallel Computing and Optimization Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2307.11908

openalex publication_date 2023/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order power method for tensor Z-eigenvalue problems. We analyze the asymptotic convergence of the method, determining the range of extrapolation parameters that induce acceleration, as well as the parameter that gives the optimal convergence rate. We then introduce an automated method to dynamically approximate the optimal parameter, and demonstrate it's efficiency when the base iteration is run with either static or adaptively set shifts. Our numerical results on both even and odd order tensors demonstrate the theory and show we achieve our theoretically predicted acceleration.

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• Quantum estimates for classical polynomial optimization
• Characteristic polynomials of tensors via Grassmann integrals and distributions of roots for random Gaussian tensors

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