# PRECONDITIONING $C^1$-QUADRATIC SPLINE COLLOCATION METHOD OF ELLIPTIC EQUATIONS BY FINITE DIFFERENCE METHOD

• Woo, Gyung-Soo (DEPARTMENT OF MATHEMATICS, CHANGWON NATIONAL UNIVERSITY) ;
• Kim, Seok-Chan (DEPARTMENT OF MATHEMATICS, CHANGWON NATIONAL UNIVERSITY)
• Published : 2001.02.01

#### Abstract

We discuss a finite difference preconditioner for the$C^1$ Lagrance 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.

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