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Numerical solution of some algebraic problems arising in the theory of stability. (English. Russian original) Zbl 0568.65026

U.S.S.R. Comput. Math. Math. Phys. 24, No. 2, 1-6 (1984); translation from Zh. Vychisl. Mat. Mat. Fiz. 24, No. 3, 339-347 (1984).
The author suggests iterative methods for solving particular matrix problems in the stability theory, such as calculating a square root of a complex matrix having the eigenvalues only in the right half of the complex plane, and solving the equation \(AX+XB=F\), where A and B are square and F is rectangular. He also gives integral representations of the solutions.
Reviewer: S.Zlobec

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
65F10 Iterative numerical methods for linear systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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