A fast algorithm for the multiplication of generalized Hilbert matrices with vectors

Author:
A. Gerasoulis

Journal:
Math. Comp. **50** (1988), 179-188

MSC:
Primary 65F30; Secondary 65D30, 65R20

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917825-9

MathSciNet review:
917825

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Abstract | References | Similar Articles | Additional Information

Abstract: The existence of a fast algorithm with an time complexity for the multiplication of generalized Hilbert matrices with vectors is shown. These matrices are defined by , , , , where and are distinct points in the complex plane and , . The major contribution of the paper is the stable implementation of the algorithm for two important sets of points, the Chebyshev points and the *n*th roots of unity. Such points have applications in the numerical approximation of Cauchy singular integral equations. The time complexity of the algorithm, for these special sets of points, reduces to .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917825-9

Keywords:
Generalized Hilbert matrices,
fast algorithms,
computational complexity,
singular integrals

Article copyright:
© Copyright 1988
American Mathematical Society