CONVERGENCE-RATES FOR MOMENT COLLOCATION SOLUTIONS OF LINEAR OPERATOR-EQUATIONS

Given a linear operator equation Kf = g with data g(x(i)), i = 1,..., n, we consider the general moment collocation solution defined as the function f(n) that minimizes \\Pf(n)\\(2) over a Hilbert space, subject to Kf(n)(x(i)) = g(x(i)), i = 1,...,n. Here P is an orthogonal projection with a finite dimensional null space. In the case of P = I, the identity, it is known that if a certain kernel depending on K is continuous, then f(n) --> f(0), the true solution, as the maximum subinterval width --> 0. Moreover, if the kernel satisfies a smoothness condition, then rates of convergence are known. In this paper we extend these results to the case with general P.