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Comparison of discrete solutions on the eigenvalue problem for a Fredholm operator. (English) Zbl 0619.65135
Variational methods in engineering, Proc. 2nd Int. Conf., Southampton/Engl. 1985, 29-37 (1985).
[For the entire collection see Zbl 0618.00010.]
Different numerical procedures are compared, for the solution of the eigenvalue problem for a Fredholm integral operator K.
Our interest for this problem originates from the study of ill-posed linear inverse problems of the type \((Kf)(x)=g(x)\) in which the solution f is unstable for small variations - e.g. measurement errors - of the data g.
The paper compares different discretization techniques which are appropriate for this purpose (Courant’s method, quadrature methods, Galerkin techniques) and, for two particular kernels, compares theoretical and observed convergence rates.
MSC:
65R20 Numerical methods for integral equations
45C05 Eigenvalue problems for integral equations