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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v43.i2.10
pages 1-6

On the Choice of the Initial Approximation in Iterative Solution Algorithm of Equation X − ATX−1A = Q

Vladimir B. Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine


The solution algorithm of matrix equation has been considered. In this algorithm the initial approximation is constructed by using linear matrix inequalities. For improving the obtained approximation the Newton procedure has been used. By the examples there has been shown the algorithm efficiency also in cases when the eigenvalues of the matrix pencil associated with this equation lay on the unit circle, i.e., when using the traditional algorithm is very problematic.

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