The goal of this paper is to improve Rump's method using grouped block matrix computations. We first show that upper bounds of the residual of Cholesky decomposition can be reduced by block computations. Based on the new bounds, positive definiteness can be verified for a wide range of ...
美 英 un.正定性 英汉 网络释义 un. 1. 正定性
Positive Type and Positive Definite Functions on Matrix Valued Group Algebras Article 20 September 2020 Positive definiteness of Hadamard exponentials and Hadamard inverses Article 13 July 2024 Data availability (1) Data sharing is not applicable to this article as no datasets were generated or ...
positive definiteness: xAx>0forallnonzerovectorsx.It is rather difficult to determine whether a matrix is positive definite. Fortunately, there are more easily verified criteria for identifying members of this important class. First, all eigenvalues of a positive definite matrix are positive. This ...
Positive semi-definite 2×2 block matrices and norm inequalities Let M = [ A X X B ] ∈ C 2 n × 2 n mathContainer Loading Mathjax be positive semi-definite 2×2 2 × 2 mathContainer Loading Mathjax block matrix, whe... M Gumus,J Liu,S Raouafi,... - 《Linear Algebra & Its...
Besides, it is difficult to check positive definiteness for a large matrix, but usually not for the small ones. See Chapter 8 for an important example. (2) A symmetric positive definite matrix has n eigenvalues which are all real positive numbers. (3) The determinant of a symmetric positive...
Copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints The necessity of the existence of a copositive matrix C such that Q A′CA is positive semidefinite is proved only under various additional hypotheses regarding the size or rank of A, and counte...
The methods outlined here might give different results for the same matrix. Since both calculations involve round-off errors, each algorithm checks the definiteness of a matrix that is slightly different fromA. In practice, the use of a tolerance is a more robust comparison method, since eigenval...
The nuclear norm is widely used to induce low-rank solutions for many optimization problems with matrix variables. Recently, it has been shown that the aug... J Yang - 《Mathematics of Computation》 被引量: 276发表: 2013年 Solving Multiple-Block Separable Convex Minimization Problems Using Two...
The definition of the extended sub metapositive definiteness matrix and n×n real matrix meta Volterra multiplicator are given. 推广了亚次正定矩阵的概念 ,即广义亚次正定矩阵和实方阵的次Volterra乘子的概念 ,讨论并给出了广义亚次正定矩阵的一些基本性质及实方阵存在次Volterra乘子的条件。2...