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 Preconditioning $C^1$-quadratic spline collocation method of elliptic equations by finite difference method Bull. Korean Math. Soc. 2001 Vol. 38, No. 1, 17-27 Gyungsoo Woo and Seokchan Kim Changwon National University, Changwon National University Abstract : 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. Keywords : preconditioning, collocation, elliptic equation MSC numbers : 65N35, 65F05, 65F10 Downloads: Full-text PDF