Abstract In this paper, we investigate the effective condition numbers for the generalized Sylvester equation （AX - YB, DX - YE） = （C,F）, where A,D ∈ Rm×m B,E ∈ Rn×n and C,F ∈ Rm×n. We apply the ...Abstract In this paper, we investigate the effective condition numbers for the generalized Sylvester equation （AX - YB, DX - YE） = （C,F）, where A,D ∈ Rm×m B,E ∈ Rn×n and C,F ∈ Rm×n. We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation, which requires （9（m2n ＋ mn2） flops, comparing with （-O（m3 ＋ n3） flops for the generalized Schur and generalized Hessenberg- Schur methods for solving the generalized Sylvester equation. Numerical examples illustrate the sharpness of our perturbation bounds.展开更多
This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump coefficients.By analyzing the eigenvalue distrib...This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump coefficients.By analyzing the eigenvalue distribution of the RASHO preconditioner,we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11001045,10926107 and 11271084)Specialized Research Fund for the Doctoral Program of Higher Education of MOE(Grant No. 20090043120008)+4 种基金Training Fund of NENU’S Scientific Innovation Project of Northeast Normal University(Grant No. NENU-STC08009)Program for Changjiang Scholars and Innovative Research Team in Universitythe Programme for Cultivating Innovative Students in Key Disciplines of Fudan University(973 Program Project)(Grant No. 2010CB327900)Doctoral Program of the Ministry of Education(Grant No.20090071110003)Shanghai Science & Technology Committee and Shanghai Education Committee(Dawn Project)
文摘Abstract In this paper, we investigate the effective condition numbers for the generalized Sylvester equation （AX - YB, DX - YE） = （C,F）, where A,D ∈ Rm×m B,E ∈ Rn×n and C,F ∈ Rm×n. We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation, which requires （9（m2n ＋ mn2） flops, comparing with （-O（m3 ＋ n3） flops for the generalized Schur and generalized Hessenberg- Schur methods for solving the generalized Sylvester equation. Numerical examples illustrate the sharpness of our perturbation bounds.
基金supported by Research Starting Funds for Imported Talents of Ningxia University(BQD2014010)the Natural Science Foundations of China(No.11501313).The second author is supported by the Natural Science Foundations of China(No.11271298 and No.11362021).
文摘This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump coefficients.By analyzing the eigenvalue distribution of the RASHO preconditioner,we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.
