This paper derives a solution to the equation\rho (u, s) = N_{0}h(s, u) + \int_{0}^{T} \rho (t, s)h(t, u) dt, for the case in which the kernel is the covariance function of a stationary random process whose spectral density is a rational function of frequency.

Occasionally in the numerical solution of elliptic partial differential equations the rate of convergence of relaxation methods to the solution is adversely affected by the relative proximity of certain points in the grid. It has been proposed that the removal of the unknown functional values at these points by Gaussian elimination may accelerate the convergence. By application of the Perron-Frobenius theory of non-negative matrices it is shown that the rates of convergence of the Jacobi-Richardson and Gauss-Seidel iterations are not decreased and could be increased by this elimination. Although this may indicate that the elimination could improve the convergence rate for overrelaxation, it is still strictly an unsolved problem.