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A GENERALIZATION OF ROUTH-HURWITZCRITERION
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作者 YANG Xiaojing (Department of Mathematics, Tsinghua University, Beijing 100084, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1999年第1期45-48,共4页
This paper presents a criterion for a polynomial to be non-unstable and for the calculation of the number of eigenvalues which have zero real parts and negative real parts.It generalizes the Routh-Hurwitz criterion an... This paper presents a criterion for a polynomial to be non-unstable and for the calculation of the number of eigenvalues which have zero real parts and negative real parts.It generalizes the Routh-Hurwitz criterion and is very convenient in many applications. 展开更多
关键词 routh-hurwitz criterion stable polynomial.
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Routh-Hurwitz判别法的一个应用 被引量:5
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作者 杨小京 《清华大学学报(自然科学版)》 EI CAS CSCD 北大核心 1996年第2期79-82,共4页
Routh-Hurwitz判别定理在理论上和工程应用中有着广泛的应用。但由于在实际应用中,往往会出现临界情形,即R-H条件中的某些严格不等式不能满足,而较弱的不严格能够成立。本文针对此问题给出了特征多项式的一些零点处... Routh-Hurwitz判别定理在理论上和工程应用中有着广泛的应用。但由于在实际应用中,往往会出现临界情形,即R-H条件中的某些严格不等式不能满足,而较弱的不严格能够成立。本文针对此问题给出了特征多项式的一些零点处于临界状态的所谓半稳定时的一种判别方法,这种方法弥补了R-H定理的应用局限性,在理论上和实际应用上是简单方便的,可以看成为R-H定理的补充。 展开更多
关键词 稳定多项式 半稳定多项式 R-H判别法
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Schur Complement Based Preconditioners for Twofold and Block Tridiagonal Saddle Point Problems
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作者 Mingchao Cai Guoliang Ju Jingzhi Li 《Communications in Mathematical Research》 CSCD 2024年第2期214-244,共31页
In this paper,we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems.One type of the preconditioners are based on the nested(or recursive)Schur complement... In this paper,we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems.One type of the preconditioners are based on the nested(or recursive)Schur complement,the other is based on an additive type Schur complement after permuting the original saddle point systems.We analyze different preconditioners incorporating the exact Schur complements.We show that some of them will lead to positively stable preconditioned systems if proper signs are selected in front of the Schur complements.These positive-stable preconditioners outperform other preconditioners if the Schur complements are further approximated inexactly.Numerical experiments for a 3-field formulation of the Biot model are provided to verify our predictions. 展开更多
关键词 Schur complement block tridiagonal systems positively stable preconditioners routh-hurwitz stability criterion.
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