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VOL. 17 | 1988 On the asymptotic distribution of the eigenvalues of discretizations of a compact operator

Abstract

It is well known that bounds on the asymptotic decay rate of the eigenvalues of the symmetric integral operator with kernel k(s,t) may be obtained from the smoothness of k(s,t) [1,4,7,9,11]. Some recent numerical results suggested that these bounds also applied to the eigenvalues of matrices with entries $K_{mn} = k(s_m,t_n)$ that occur in various discretizations of the continuous operator. This note shows that, in certain common situations, this is indeed the case.

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Published: 1 January 1988
First available in Project Euclid: 18 November 2014

zbMATH: 0678.47013
MathSciNet: MR1000358

Rights: Copyright © 1988, Centre for Mathematical Analysis, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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Vol. 17 • 1 January 1988
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