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

Author:

Gerasoulis A.

Abstract

The existence of a fast algorithm with an O A ( n ( log n ) 2 ) {O_A}(n{(\log n)^2}) time complexity for the multiplication of generalized Hilbert matrices with vectors is shown. These matrices are defined by ( B p ) i , j = 1 / ( t i s j ) p {({B_p})_{i,j}} = 1/{({t_i} - {s_j})^p} , i , j = 1 , , n i,j = 1, \ldots ,n , p = 1 , , q p = 1, \ldots ,q , q n q \ll n , where t i {t_i} and s i {s_i} are distinct points in the complex plane and t i s j {t_i} \ne {s_j} , i , j = 1 , , n i,j = 1, \ldots ,n . The major contribution of the paper is the stable implementation of the algorithm for two important sets of points, the Chebyshev points and the nth 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 O A ( n log n ) {O_A}(n\log n) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference23 articles.

1. Addison-Wesley Series in Computer Science and Information Processing;Aho, Alfred V.,1975

2. M. Comninou, "The interface crack," J. Appl. Mech., Transactions of ASME, 1977, pp. 631-636.

3. A generalized conjugate gradient method for nonsymmetric systems of linear equations;Concus, Paul,1976

4. Prentice-Hall Series in Automatic Computation;Björck, Ȧke,1974

5. The numerical treatment of singular integral equations—a review;Elliott, David,1982

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