Roch, Steffen; Silbermann, Bernd Non-strongly converging approximation methods. (English) Zbl 0696.65055 Demonstr. Math. 22, No. 3, 651-676 (1989). To solve operator equations of the form (*) \(Ax=y\) one may consider the problem \((+)\) \(P_{\tau}Ax_{\tau}=P_{\tau}y\), where \(P_{\tau}\) are projection operators. If there exists a \(\tau_ 0\) such that for \(\tau \geq \tau_ 0\) the problem \((+)\) has a unique solution \(x_{\tau}\), the convergence \(x_{\tau}\to x\) must be guaranteed. There are interesting examples, e.g. in the case of integral equations on the space of bounded measurable functions where the convergence only holds in a weaker sense. This observation leads the authors to the definition of the convergence with respect to a family of projections. Convergent approximation methods for (*) in this weaker sense are studied. The result is applied to the Wiener-Hopf integral equation using a composite quadrature rule method. Reviewer: W.Petry Cited in 12 Documents MSC: 65J10 Numerical solutions to equations with linear operators 65R20 Numerical methods for integral equations 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 47A50 Equations and inequalities involving linear operators, with vector unknowns Keywords:operator equations; projection operators; convergence; Convergent approximation methods; Wiener-Hopf integral equation; quadrature rule method PDFBibTeX XMLCite \textit{S. Roch} and \textit{B. Silbermann}, Demonstr. Math. 22, No. 3, 651--676 (1989; Zbl 0696.65055) Full Text: DOI