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Bull. Korean Math. Soc. 2001; 38(1): 17-27

Printed March 1, 2001

Copyright © The Korean Mathematical Society.

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

Gyungsoo Woo and Seokchan Kim

Changwon National University, Changwon National University

Abstract

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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

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