Work

A Fast Projected Gradient Algorithm for Quaternion Hermitian Eigenvalue Problems

Year: 2025

Type: article

Abstract: In this paper, based on the novel generalized Hamilton-real (GHR) calculus, we propose for the first time a quaternion Nesterov accelerated projected gradient algorithm for computing the dominant eigenvalue and eigenvector of quaternion Hermitian matrices. By introducing momentum terms and look-ahead updates, the algorithm achieves a faster convergence rate. We theoretically prove the convergence of the quaternion Nesterov accelerated projected gradient algorithm. Numerical experiments show that the proposed method outperforms the quaternion projected gradient ascent method and the traditional algebraic methods in terms of computational accuracy and runtime efficiency.

Source: Mathematics

DOI: 10.3390/math13060994

Authors: Shan-Qi Duan, Qing-Wen Wang

Institution: Shanghai University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China