The numerical solutions of the eigenvalue problem for compact integral operators
KENDALL E. ATKINSON · Transactions of the American Mathematical Society · 1967
Introduction.With linear integral equations of the second kind, an important method for their numerical solution[10], is to replace the integral operator with an approximating numerical integration operator.The resulting equation is equivalent to a finite linear system, and linear systems are relatively easy to treat.In [1], [2], the method is lifted into a functional analysis framework, and in this setting a complete error analysis is given.More precisely, the following are the basic assumptions of [1] and also of this paper.Al. A1 and Kn, n-1, are linear operators on Zinto A", where Xis a Banach space.A2.Knx -> Kx as n -> oo, for all x e X. A3.The sequence {Kn} is compact in aggregate, i.e., the set E(X0,K) = ±-( (X-K)-idX ¿"l J|A-A0|=£