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Two efficient algorithms for the commutative quaternion equality constrained least squares problem
Journal of Computational and Applied Mathematics. 2026. Vol. 474. Article 116964.
Zhang D., Jiang T., Васильев В. И., Wang G.
With the development of the applied discipline of commutative quaternions, the commutative quaternion equality constrained least squares (CQLSE) problem is gaining more and more attention as an effective tool. However, the knowledge gap in numerous CQLSE problems is now unresolved. This paper, by means of the complex representation matrix of a commutative quaternion matrix, first studies the QR decomposition and generalized singular value decomposition (GSVD) of commutative quaternion matrices, and gives the corresponding theorems and algorithms. In addition, the algorithms for solving the CQLSE problem based on QR decomposition and GSVD of commutative quaternion matrices are given in this paper. Finally, numerical experiments show the effectiveness of the algorithms proposed in this paper.
Publication based on the results of:
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Added: September 24, 2026
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Added: September 21, 2026
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This study explores the incorporation of specialized self-attention mechanisms into deep learning architectures, with a particular emphasis on segmenting human iris and pupil regions in infrared images. In this work, we present some modified versions of nonlocal blocks designed to enhance self-attentive properties while addressing the distinct characteristics of infrared imaging data. By applying these customized ...
Added: September 21, 2026
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Abstract—Existing word embedding models represent each word with two real-valued vectors: central and context. This happens because of words relations asymmetric nature and requires more time and data for training. We introduce a new approach based on asymmetric relations that uses the advantages of global vectors model. Due to the reduction of asymmetric information impact ...
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