University of TabrizComputational Methods for Differential Equations2345-39827120190101On the solving of matrix equation of Sylvester type961048308ENFikretAlievInstitute of Applied Mathematics,
Baku State University, Baku, AzerbaijanVladimirLarinInstitute of Mechanics of the Academy of
Sciences of Ukraine, Ukraine, KievJournal Article20180719A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the given matrix. For this, an algorithm for constructing a general solution of the Sylvester matrix equation is used. The effectiveness of the proposed approaches is illustrated on the examples.https://cmde.tabrizu.ac.ir/article_8308_8490b775c091e584aa7755c033bcd854.pdf