Abstract
The calculation of eigenvalues of matrices is the classical problem of linear algebra. Construction of standard programs for its solution comes across serious difficulties if matrices are non-symmetric. One can easily construct examples of matrices of not very high order whose spectrum, being calculated by computer, fills two-dimensional domains of a complex plane. In the automatic regulation theory and in the stability theore one often has to find out whether the whole spectrum lies in the left-hand half-plane or not (Hurwitz problem). Described and grounded in the paper is a computably stable algorithm for the solution of this problem, requiring no calculations of either eigenvalues or Hurwitz determinants.
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