Sheehan Olver.

Title: GMRES for oscillatory differential equations

Abstract
	We consider using the generalized minimum residual method (GMRES) for
computing oscillatory ordinary differential equations.  This method minimizes the 
residual of the Krylov subspace associated with the differential formulation of 
the equation.  It turns out that this method actually improves as the oscillations 
increase, at the same asymptotic order as the number of iterations used.   
Standard Krylov subspace theory doesn't apply, since differential operators are 
unbounded.  Thus we must also prove convergence of this approximation.  This 
follows from a new theorem which proves conditions in which a function can be
approximated pointwise by its own derivatives.