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Then we propose a power method for computing the dominant eigenvalue of a dual quaternion Hermitian matrix. For a strict dominant eigenvalue, we show the sequence generated by the power method converges to the dominant eigenvalue and its corresponding eigenvector linearly. For a general dominant eigenvalue, we establish linear convergence of the standard part of the dominant eigenvalue. Based upon these, we reformulate the simultaneous localization and mapping problem as a rank-one dual quaternion completion problem. A two-block coordinate descent method is proposed to solve this problem. One block has a closed-form solution and the other block is the best rank-one approximation problem of a dual quaternion Hermitian matrix, which can be computed by the power method. Numerical experiments are presented to show the efficiency of our proposed power method.<\/jats:p>","DOI":"10.1007\/s10915-024-02561-x","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T05:01:28Z","timestamp":1717477288000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["A Power Method for Computing the Dominant Eigenvalue of a Dual Quaternion Hermitian Matrix"],"prefix":"10.1007","volume":"100","author":[{"given":"Chunfeng","family":"Cui","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1112-5250","authenticated-orcid":false,"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"2561_CR1","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1002\/rob.20178","volume":"24","author":"M Bryson","year":"2007","unstructured":"Bryson, M., Sukkarieh, S.: Building a robust implementation of bearing\u2014only inertial SLAM for a UAV. 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