Inverse unitary eigenproblems and related orthogonal functions |
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Authors: | Heike Faßbender |
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Institution: | Universit?t Bremen, Fachbereich 3 – Mathematik und Informatik, D-28334 Bremen, Germany; e-mail: heike@mathematik.uni-bremen.de, DE
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Abstract: | Summary. This paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions. In particular,
the inverse eigenvalue problems for unitary Hessenberg matrices and for Schur parameter pencils are considered. The Szeg?
recursion is known to be identical to the Arnoldi process and can be seen as an algorithm for solving an inverse unitary Hessenberg
eigenvalue problem. Reformulation of this inverse unitary Hessenberg eigenvalue problem yields an inverse eigenvalue problem
for Schur parameter pencils. It is shown that solving this inverse eigenvalue problem is equivalent to computing Laurent polynomials
orthogonal on the unit circle. Efficient and reliable algorithms for solving the inverse unitary eigenvalue problems are given
which require only O() arithmetic operations as compared with O() operations needed for algorithms that ignore the structure of the problem.
Received April 3, 1995 / Revised version received August 29, 1996 |
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Keywords: | Mathematics Subject Classification (1991):65F99 |
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