Summary
We study Vandermonde matrices whose nodes are given by a Van der Corput sequence on the unit circle. Our primary interest is in the singular values of these matrices and the respective (spectral) condition numbers. Detailed information about multiplicities and eigenvectors, however, is also obtained. Two applications are given to the theory of polynomials.
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Dedicated to R. S. Varga on the occasion of his sixtieth birthday
Research of A. C. supported by the Fundación Andes, Chile, and by the German Academic Exchange Service (DAAD), Federal Republic of Germany
Research of W. G. supported, in part, by the National Science Foundation, USA, (Grant CCR-8704404)
Research of S. R. supported by the Fondo Nacional de Desarollo Cientßfico y Tecnológico (FONDECYT), Chile, (Grant 237/89), by the Universidad Técnica F. Santa Marßa, Valparaßso, Chile, (Grant 89.12.06), and by the German Academic Exchange Service (DAAD), Federal Republic of Germany
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Córdova, A., Gautschi, W. & Ruscheweyh, S. Vandermonde matrices on the circle: Spectral properties and conditioning. Numer. Math. 57, 577–591 (1990). https://doi.org/10.1007/BF01386429
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DOI: https://doi.org/10.1007/BF01386429