Preconditioning $C^1$-quadratic spline collocation method of elliptic equations by finite difference method

摘要

We discuss a finite difference preconditioner for the $C^1$ Lagrange quadratic spline collocation method for a uniformly elliptic operator with homogeneous Dirichlet boundary conditions. Using the generalized field of values argument, we analyzed eigenvalues of the matrix preconditioned by the matrix corresponding to a finite difference operator with zero boundary condition.