A fast but unstable orthogonal triangularization technique for Toeplitz matrices (Q1822200)
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scientific article; zbMATH DE number 4001303
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fast but unstable orthogonal triangularization technique for Toeplitz matrices |
scientific article; zbMATH DE number 4001303 |
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A fast but unstable orthogonal triangularization technique for Toeplitz matrices (English)
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1987
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An algorithm A by \textit{D. R. Sweet} [Numer. Math. 43, 1-21 (1984; Zbl 0504.65017)] for the QR decomposition of Toeplitz matrices T is compared with two other algorithms B and C of \textit{E. H. Bareiss} [ibid. 13, 404- 424 (1969; Zbl 0174.204)] and \textit{W. F. Trench} [SIAM J. Appl. Math. 12, 515-522 (1964; Zbl 0131.360)]. It is shown that A may lead to inaccurate decomposition if certain submatrices in T are ill-conditioned. A is compared with B and C using four different classes of examples. Merits and failings of each method are pointed out.
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ill-conditioned submatrices
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QR decomposition
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Toeplitz matrices
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