본문 바로가기
KERD
논문KCI 등재

Eigenvalues for the semi-circulant reconditioning of elliptic operators with the variable coefficients

이용훈|김상동|김회섭
대한수학회 (The Korean Mathematical Society)|2007.05|대한수학회지 (Journal of the KMS)|제44권 제3호|pp. 627-645

0

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

We investigate the eigenvalues of the semi-circulantpreconditioned matrix for the finite difference schemecorresponding to the second-order elliptic operatorwith the variable coefficients given byL_v u := -Delta u + a(x,y) u_x + b(x,y) u_y + d(x,y) u,where a and b are continuously differentiable functionsand d is a positive bounded function.The semi-circulant preconditioning operator L_c u is constructedby using the leading term of L_v u plus the constant reaction term suchthat L_c u:= -Delta u + d_c u.Using the field of values arguments,we show that the eigenvalues of the preconditioned matrix areclustered at some number. Some numerical evidences are also provided.

참고문헌 (17)

  1. "A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part", 35(2-4), pp.351~372 (2004)
  2. "Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems", 24(3), pp.603~626 (2003)
  3. "Blocktriangular and skew-Hermitian splitting methods forpositive-definite linear systems", 26(3), pp.844~863 (2005)
  4. "Preconditioned HSS methods for the solution of non-Hermitianpositive definite linear systems and applications to the discreteconvection-diffusion equation", 99(3), pp.441~484 (2005)
  5. "Circulant preconditioners for elliptic problems", pp.77~ (1992)
  6. "A family of block preconditioners for block systems", pp.1218~ (1992)
  7. "Conjugate gradient methods for Toeplitz systems", 38(3), pp.427~482 (1996)
  8. "Block-circulant preconditioners for systems arising from discretization of the three-dimensional convection-diffusion equation,Proceedings of the 9th International Congress on Computational and Applied Mathematics", 140(1-2), pp.143~158 (2002)
  9. "Iterative methods for cyclically reduced nonselfadjoint linear systems", pp.671~ (1990)
  10. "Iterative methods for cyclically reduced nonselfadjoint linear systems", pp.215~ (1991)
  11. "Block orderings fortensor-product grids in two and three dimensions", 30(2), pp.93~111 (2002)
  12. "On the preconditioning of matrices with skew-symmetric splittings Mathematical journey through analysis, matrix theory and scientific computation", 25(1-4), pp.223~239 (2000)
  13. "Numerical range,The field of values of linear operators and matrices" (1997), Universitext. Springer-Verlag, New York
  14. "A semi-circulant preconditioner for the convection-diffusion equation", 81(2), pp.211~248 (1998)
  15. "Semicirculant preconditioning of elliptic operators", 41(2), pp.767~795 (2003)
  16. "The finite difference method in partial differential equations" (1980), Ltd
  17. "Circulant and skew-circulant splitting methods for Toeplitz systems,Proceedings of the 6th Japan-China Joint Seminar on Numerical Mathematics", 159(1), pp.101~108 (2003)

관련 논문AI추천

THE EIGENVALUE PROBLEM AND A WEAKER FORM OFTHE PRINCIPLE OF SPATIAL AVERAGINGHyukjinKwean한국수학교육학회 · 이론수학과 교직수학2002 · 제9권 제1호The solvability conditions for a class of constrained inverse eigenvalue problem of antisymmetric matricesLei Zhang, Xiao-ping Pan, Xi-yan Hu대한수학회 · 대한수학회지2006 · 제43권 제1호ON THE SPECTRAL PROPERTIES OF THE SCHR[수식]ODINGER OPERATOR WITH A MATRIX POTENTIALCoskan, Karakilic장전수학회 · Advanced Studies in Contemporary Mathematics2009 · 제19권 제2호A note on scattering operator symbols for elliptic wave propagation김정훈대한수학회 · 대한수학회논문집2002 · 제17권 제2호Modified incomplete Cholesky factorization preconditioners for a symmetric positive definite matrix윤재헌, 한유두대한수학회 · 대한수학회보2002 · 제39권 제3호Computation of eigenvalues and fundamental solutions of a fourth-order boundary value problemErdogan Sen, Serkan Araci장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제4호

이 간행물의 다른 논문 (16건)

Group determinant formulas and class numbers of cyclotomic fields안재현, 정환엽pp. 499-509Persistence of Periodic Trajectories of Planar Systems under two Parametric PerturbationsOmid RabieiMotlagh, Zahra Afsharnejadpp. 511-523Asymptotic normality of estimator in non-parametric model under censored samplesQian-Ru Li, Si-Li Niupp. 525-539Endpoint estimates for multilinear integral operatorsLiu Lanzhepp. 541-564A refinement of the classical Clifford inequalityHristo Ilievpp. 565-583
원문 보기