Let ||x||μ be a norm defined on linear space Cm, then a matrix A∈Cm×n, as a linear operator on Cn, has a norm correspondingly. We denote by Pμ （A） the condition number of A, namely Pμ（A） = |A|μ|A-1|μ. T...Let ||x||μ be a norm defined on linear space Cm, then a matrix A∈Cm×n, as a linear operator on Cn, has a norm correspondingly. We denote by Pμ （A） the condition number of A, namely Pμ（A） = |A|μ|A-1|μ. This is a basic concept in numerical algebra and also very important in some other fields of numerical analysis. Under certain circumstances, someone takes the ratio |λz|/|λ1| as the condition number, where λm and λ1 are the largest and smallest eigenvalue of A by norm. The relationship between them will be presented below.展开更多
A domain decomposition method with many subregions and cross points is discussed.At each cross point, a subregion is selected to cover it, called a covering subdomain. Thecovering subdomains of different cross points ...A domain decomposition method with many subregions and cross points is discussed.At each cross point, a subregion is selected to cover it, called a covering subdomain. Thecovering subdomains of different cross points do not intersect each other. The decompositionmethod in this paper is realized through a procedure of a combination of solving Dirichletproblems, mixed problems on subdomains and Dirichlet problems on the covering sub-domains. The idea of the two-subdomain Schwarz alternating method and two-subdomain paralleliterative decomposition method is used. There is no continuous counterpart of this algorithm,and only the discrete problem is discussed. This algorithm is highly parallel and has localcommunication property, and it suits to arbitrarily many subdomains decomposition.展开更多
文摘Let ||x||μ be a norm defined on linear space Cm, then a matrix A∈Cm×n, as a linear operator on Cn, has a norm correspondingly. We denote by Pμ （A） the condition number of A, namely Pμ（A） = |A|μ|A-1|μ. This is a basic concept in numerical algebra and also very important in some other fields of numerical analysis. Under certain circumstances, someone takes the ratio |λz|/|λ1| as the condition number, where λm and λ1 are the largest and smallest eigenvalue of A by norm. The relationship between them will be presented below.
文摘A domain decomposition method with many subregions and cross points is discussed.At each cross point, a subregion is selected to cover it, called a covering subdomain. Thecovering subdomains of different cross points do not intersect each other. The decompositionmethod in this paper is realized through a procedure of a combination of solving Dirichletproblems, mixed problems on subdomains and Dirichlet problems on the covering sub-domains. The idea of the two-subdomain Schwarz alternating method and two-subdomain paralleliterative decomposition method is used. There is no continuous counterpart of this algorithm,and only the discrete problem is discussed. This algorithm is highly parallel and has localcommunication property, and it suits to arbitrarily many subdomains decomposition.
