An Efficient QR Algorithm for a Hessenberg Submatrix of a Unitary Matrix
نویسندگان
چکیده
We describe an efficient procedure for implementing the Hessenberg QR algorithm on a class of matrices that we refer to as subunitary matrices. This class includes the set of Szegő-Hessenberg matrices, whose characteristic polynomials are Szegő polynomials, i.e., polynomials orthogonal with respect to a measure on the unit circle in the complex plane. Computing the zeros of Szegő polynomials is important in time series analysis and in the design and implementation of digital filters. For example, these zeros are the poles of autoregressive filters.
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