Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations Original Research Article

In the work of solving a uniformly elliptic differential equations Au:=−Δu+a1ux+a2uy+a0u=f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix when a full finite element preconditioning is considered.