Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 9 Issue 2
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- Pages.439-448
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
THE STEEPEST DESCENT METHOD AND THE CONJUGATE GRADIENT METHOD FOR SLIGHTLY NON-SYMMETRIC, POSITIVE DEFINITE MATRICES
- Shin, Dong-Ho (Department of Mathematics Inje University) ;
- Kim, Do-Hyun (Department of Mathematics Education Cheju University) ;
- Song, Man-Suk
- Published : 1994.04.01
Abstract
It is known that the steepest descent(SD) method and the conjugate gradient(CG) method [1, 2, 5, 6] converge when these methods are applied to solve linear systems of the form Ax = b, where A is symmetric and positive definite. For some finite difference discretizations of elliptic problems, one gets positive definite matrices that are almost symmetric. Practically, the SD method and the CG method work for these matrices. However, the convergence of these methods is not guaranteed theoretically. The SD method is also called Orthores(1) in iterative method papers. Elman [4] states that the convergence proof for Orthores(
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