Chansangiam, Pattrawut
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Preferred name
Chansangiam, Pattrawut
Alternative Name
Chansangiam, P.
Main Affiliation
Email
pattrawut.ch@kmitl.ac.th
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Item type:Publication, Least-squares solutions of generalized linear systems and the matrix equation AXB = C under the general semi-tensor products(2026-01-01); Zhang, YangWe investigate least-squares (LS) solutions of Sylvester-type matrix equations formulated via the general semi-tensor product (GSTP) of matrices. In particular, we consider generalized linear systems of the form A (Formula presented) x = B, where A and B are given rectangular matrices and x is an unknown column vector, with k denoting the GSTP that extends both the conventional matrix product and the semi-tensor product. By analyzing the derivative of the LS error associated with the equation, we show that LS solutions can be obtained by solving an equivalent linear system under the usual matrix product. Using matrix partitioning techniques, these results are further extended to several Sylvester-type equations, including A (Formula presented) X = B, X (Formula presented) A = B. and A (Formula presented) X x B = C, where X is an unknown matrix of compatible size. This framework unifies the classical and semi-tensor product cases under a generalized algebraic setting. Furthermore, we develop a gradient-descent iterative algorithm to compute approximate LS solutions efficiently. Numerical experiments confirm the convergence, capability, and effectiveness of the proposed method. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Exact and least-squares solutions of a generalized Sylvester-transpose matrix equation over generalized quaternions(2024-01-01)