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On a Sturm sequence of polynomials for unitary Hessenberg matrices. (English) Zbl 0839.65044

The mathematical structure of unitary Hessenberg matrices is closely analogous to that of real symmetric matrices. This paper presents a unitary analogue of the bisection method for symmetric tridiagonal matrices. The basis of the analogue is that the number of eigenvalues of a unitary Hessenberg matrix between \(\xi\) and \(\eta\) on the unit circle can be determined by a unitary Sturm sequence of polynomials for the unitary Hessenberg matrix.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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