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Bibliographic Details
Main Authors: Ochiai, Hiroyuki, Sekiguchi, Yoshiyuki, Waki, Hayato
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.16689
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Table of Contents:
  • We observe that the characteristic polynomial of a linearly perturbed semidefinite matrix can be used to give the convergence rate of alternating projections for the positive semidefinite cone and a line. As a consequence, we show that such alternating projections converge at $O(k^{-1/2})$, independently of the singularity degree. A sufficient condition for the linear convergence is also obtained. Our method directly analyzes the defining equation for an alternating projection sequence and does not use error bounds.