On the $\top$-Stein equation $X=AX^\top B+C$

Chun-Yueh Chiang; Matthew M. Lin

arxiv: 1210.5731 · v1 · pith:5VGFRVBBnew · submitted 2012-10-21 · 🧮 math.NA · cs.NA

On the top-Stein equation X=AX^top B+C

Matthew M. Lin , Chun-Yueh Chiang This is my paper

classification 🧮 math.NA cs.NA

keywords equationsteinconditionspartalgorithmanalyzecdotconsider

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We consider the $\top$-Stein equation $X = AX^\top B + C$, where the operator $(\cdot)^\top$ denotes the transpose ($\top$) of a matrix. In the first part of this paper, we analyze necessary and sufficient conditions for the existence and uniqueness of the solution $X$. In the second part, a numerical algorithm for solving $\top$-Stein equation is given under the solvability conditions.

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On the top-Stein equation X=AX^top B+C

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