The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation ...The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integrodifferential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.展开更多
Presents information on a study which dealt with Crouzeix-Raviart nonconforming finite element approximation (FEA) of Navier-Stokes equation in a plane bounded domain by using velocity-pressure mixed formulation. Nota...Presents information on a study which dealt with Crouzeix-Raviart nonconforming finite element approximation (FEA) of Navier-Stokes equation in a plane bounded domain by using velocity-pressure mixed formulation. Notations of Navier-Stokes problem and its nonconforming FEA; Description of linear nonconforming finite element spaces and their properties; Maximum-error estimates for C-R nonconforming FEA of stationary Navier-Stoke problem.展开更多
Ky Fan maximum principle is a well-known observation about traces of certain hermitian matrices. In this note, we derive a powerful extension of this claim. The extension is achieved in three ways. First, traces are r...Ky Fan maximum principle is a well-known observation about traces of certain hermitian matrices. In this note, we derive a powerful extension of this claim. The extension is achieved in three ways. First, traces are replaced with norms of diagonal matrices, and any unitarily invariant norm can be used. Second, hermitian matrices are replaced by normal matrices, so the rule applies to a larger class of matrices. Third, diagonal entries can be replaced with eigenvalues and singular values. It is shown that the new maximum principle is closely related to the problem of approximating one matrix by another matrix of a lower rank.展开更多
The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theore...The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.展开更多
文摘The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integrodifferential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.
文摘Presents information on a study which dealt with Crouzeix-Raviart nonconforming finite element approximation (FEA) of Navier-Stokes equation in a plane bounded domain by using velocity-pressure mixed formulation. Notations of Navier-Stokes problem and its nonconforming FEA; Description of linear nonconforming finite element spaces and their properties; Maximum-error estimates for C-R nonconforming FEA of stationary Navier-Stoke problem.
文摘Ky Fan maximum principle is a well-known observation about traces of certain hermitian matrices. In this note, we derive a powerful extension of this claim. The extension is achieved in three ways. First, traces are replaced with norms of diagonal matrices, and any unitarily invariant norm can be used. Second, hermitian matrices are replaced by normal matrices, so the rule applies to a larger class of matrices. Third, diagonal entries can be replaced with eigenvalues and singular values. It is shown that the new maximum principle is closely related to the problem of approximating one matrix by another matrix of a lower rank.
文摘The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.
