This paper deals with the estimation of the errors of the exact solution and the Legendre spectral solution. By using the defined elliptic projection operator, we can form the estimations of the errors. Both H and H1 norm estimations are obtained simultaneously. 讨论了精确解和Legendre谱解的误差估计,应用文中定义的椭圆投影算子,得到了H和H1模估计。
The solvability of the multidimensional total least perturbation problem in spectral norm 多重整体谱范数最小摄动问题的可解性
By spectral decomposition of a Hermitian operator and functional calculus, some important norm inequalities on complex Hilbert space are obtained. 该文给出了它的另一种证明,同时应用算子分解和函数演算,证明了复Hilbert空间上的自伴算子的几个重要范数不等式。
Some new estimates are presented for the spectral variation of two normal matrices. We prove that for any monotone unitarily invariant norm|| ·||, v ( A, B)≤|| A-B||, where A and B are both normal. 本文对正规矩阵A,B的谱变分给出一些新的估计,证明了对于任何单调酉不变范数||·||,v(A,B)≤||A-B||。
It is operator matrix, the convexity and concavity of function, the spectral decomposition of operator and functional calculus that the author is using to generalize some classical inequalities and then to give series of important operator inequalities and norm inequalities. 本文作者就是借助算子矩阵、函数的凸性和凹性、谱分解、函数演算等为工具,将许多经典的不等式加以推广并给出一系列重要的算子不等式与范数不等式。
Let A and B be two n × n symmetrizable matrices, i. e., there exists nonsingular matrices P, Q such that where are all real, and. It is proved that where denote the spectral norm; 设A,B为两个n×n可对称化矩阵,即存在非奇异矩阵P,Q使得此处均为实数,本文证明了:其中表示谱范数,而表示Frorbenius范数。
The perturbation in the discrete-time system is mapped from the continuous-time system uncertainties. And this paper also gives the estimated bounds described by the spectral norm in the equivalent discrete system under perturbation using Laplace ′ s transformation for special exponential-like uncertainty structure. 离散系统模式中的扰动是由连续系统的不确定性映象得到的,本文对特殊的指数不确定性结构,用Laplace变换方法给出了等效离散系统扰动下一个谱范数估计的界。
In this paper, the equivalence theorems about spectral radius and norm ‖·‖_2 of a class of decomposable matrix and its application are given. 文中给出一类可分解矩阵普半径与‖·‖2范数的等价性,并扼要介绍有关结果在偏微分方程差分格式稳定性讨论中的应用。