A note on the alternate trapezoidal quadrature method for Fredholm integral eigenvalue problems
The authors study the alternate trapezoidal quadrature method, introduced by \textit{A. Sidi} and \textit{M. Israeli} [J. Sci. Comput. 3, No. 2, 201--231 (1988; Zbl 0662.65122)], for the eigenvalue problem of periodic, convolution-type singular integrals. Since the discrete eigenvalues exhibit some symmetry properties that are not observed for the eigenvalues of the continuous problem, it can be shown that the method always yields eigenvalues with enlarged multiplicity. This leads to error estimates that are valid only for a subset of the discrete spectrum. To loosen this constraint the authors introduce an improved method and establish error estimates valid for the whole discrete spectrum. Numerical examples illustrate the results.
scientific article; zbMATH DE number 6153512