In this paper, we study the method of ascertaining positive-definable matrix. Weimprove the results in a paper by Hu Jiagan & Liu Xingping, and give a new method.
In this paper, the EPE_k method is considered and the positive-definable matrix isdefined. The results of this paper can also be applied to other iterative method.
Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively...Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively symmetrizable matrix is proposed in this paper. We point that for such kind of equation systems, it is possible to adopt special preconditioning CG algorithm, e.g. [1]-[3], instead of the usual iteration procedure for general non-symmetry systems, such as GMRES [3]-[4] ) BiCGSTAB [5]. Numerical tests show the new algorithm is effective for solving this kind of second order elliptic discrete systems.展开更多
The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q...The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.展开更多
An important property of the reproducing kernel of D2(Ω,ρ) is obtained and the reproducing kernels for D2(Ω,ρ) are calculated when Ω = Bn × Bn and ρ are some special functions.A reproducing kernel is used t...An important property of the reproducing kernel of D2(Ω,ρ) is obtained and the reproducing kernels for D2(Ω,ρ) are calculated when Ω = Bn × Bn and ρ are some special functions.A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on Ω×Ω.An inequality is obtained about the distance function and the pseudo-distance induced by the matrix.展开更多
文摘In this paper, we study the method of ascertaining positive-definable matrix. Weimprove the results in a paper by Hu Jiagan & Liu Xingping, and give a new method.
文摘In this paper, the EPE_k method is considered and the positive-definable matrix isdefined. The results of this paper can also be applied to other iterative method.
文摘Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively symmetrizable matrix is proposed in this paper. We point that for such kind of equation systems, it is possible to adopt special preconditioning CG algorithm, e.g. [1]-[3], instead of the usual iteration procedure for general non-symmetry systems, such as GMRES [3]-[4] ) BiCGSTAB [5]. Numerical tests show the new algorithm is effective for solving this kind of second order elliptic discrete systems.
文摘The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
基金the National Natural Science Foundation of China(No.10401024)
文摘An important property of the reproducing kernel of D2(Ω,ρ) is obtained and the reproducing kernels for D2(Ω,ρ) are calculated when Ω = Bn × Bn and ρ are some special functions.A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on Ω×Ω.An inequality is obtained about the distance function and the pseudo-distance induced by the matrix.
