Finite difference preconditioning cubic spline collocation method of elliptic equations |
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Authors: | Hong Oh Kim Sang Dong Kim Yong Hun Lee |
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Institution: | (1) Department of Mathematics, KAIST, Taejeon, Korea , KR;(2) Department of Mathematics, Teachers College, Kyungpook National University, Taegu, Korea; e-mail: skim@bh.kyungpook.ac.kr , KR |
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Abstract: | Summary. We discuss a finite difference preconditioner for the interpolatory cubic spline collocation method for a uniformly elliptic operator defined by in (the unit square) with homogeneous Dirichlet boundary conditions. Using the generalized field of values arguments, we discuss
the eigenvalues of the preconditioned matrix where is the matrix of the collocation discretization operator corresponding to , and is the matrix of the finite difference operator corresponding to the uniformly elliptic operator given by in with homogeneous Dirichlet boundary conditions. Finally we mention a bound of -singular values of for a general elliptic operator in .
Received December 11, 1995 / Revised version received June 20, 1996 |
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Keywords: | Mathematics Subject Classification (1991): 65N30 65N35 65F05 65F10 |
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