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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Improved error estimates for numerical solutions of symmetric integral equations

Author: E. Rakotch
Journal: Math. Comp. 32 (1978), 399-404
MSC: Primary 65R20
MathSciNet review: 482253
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Abstract: The most widely employed method for a numerical solution of a symmetric integral equation with kernel $ K(x,t)$ in interval $ I \equiv [a,b]$ is the replacement of the original problem by the sequence of eigenproblems

$\displaystyle {K^{(n)}}y_i^{(n)} = {\mu _{in}}y_i^{(n)},\quad {K^{(n)}} \equiv \{ {w_{jn}}K({x_{in}},{x_{jn}})\} ,\quad i = 1, \ldots ,n,$

with $ {w_{jn}} > 0$ and $ {x_{jn}} \in I,j = 1, \ldots ,n$. The eigenvectors $ y_i^{(n)}$ are further used to obtain an approximation, with improved error estimates, of the numerical eigensolution for some $ N > n$, with no necessity of computing $ {\mu _{iN}}$ and $ y_i^{(N)},i = 1, \ldots ,N$, and of constructing another matrix.

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Article copyright: © Copyright 1978 American Mathematical Society