The Chebyshev solution of the linear matrix equationAX+YB=C |
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Authors: | K Ziętak |
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Institution: | (1) Institute of Computer Science, University of Wroc aw, ul. Przesmyckiego 20, P1-51-151 Wroc aw, Poland |
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Abstract: | Summary In this paper we investigate the properties of the Chebyshev solutions of the linear matrix equationAX+YB=C, whereA, B andC are given matrices of dimensionsm×r, s×n andm×n, respectively, wherer ands. We separately consider two particular cases. In the first case we assumem=r+1 andn=s+1, in the second caser=s=1 andm, n are arbitrary. For these two cases, under the assumption that the matricesA andB are full rank, we formulate necessary and sufficient conditions characterizing the Chebyshev solution ofAX+YB=C and we give the formulas for the Chebyshev error. Then, we propose an algorithm which may be applied to compute the Chebyshev solution ofAX+YB=C for some particular cases. Some numerical examples are also given. |
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Keywords: | AMS (MOS): 41 A 50 65 D 15 CR: G 1 3 |
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