Truncated Quadrature Rules Over $(0,\infty)$ and Nyström-Type Methods

Abstract

We propose replacing the classical Gauss--Laguerre quadrature formula by a truncated version of it, obtained by ignoring the last part of its nodes. This has the effect of obtaining optimal orders of convergence. Corresponding quadrature rules with kernels are then considered and optimal error estimates are derived also for them. These rules are finally used to define stable Nyström-type interpolants for a second kind of integral equation on the real semiaxis whose solutions decay exponentially at $\infty$.