Results 31 to 40 of about 567 (182)

A note on the formulas for the Drazin inverse of the sum of two matrices

Open Mathematics, 2019
In this paper we derive the formula of (P + Q)D under the conditions Q(P + Q)P(P + Q) = 0, P(P + Q)P(P + Q) = 0 and QPQ2 = 0. Then, a corollary is given which satisfies the conditions (P + Q)P(P + Q) = 0 and QPQ2 = 0. Meanwhile, we show that the additive
Liu Xin, Yang Xiaoying, Wang Yaqiang
doaj   +1 more source

Generalization of the Sherman–Morrison–Woodbury formula involving the Schur complement [PDF]

Applied Mathematics and Computation, 2017
Let $X\in\mathbb{C}^{m\times m}$ and $Y\in\mathbb{C}^{n\times n}$ be nonsingular matrices, and let $N\in\mathbb{C}^{m\times n}$. Explicit expressions for the Moore-Penrose inverses of $M=XNY$ and a two-by-two block matrix, under appropriate conditions, have been established by Castro-González et al. [Linear Algebra Appl. 471 (2015) 353-368].
openaire   +3 more sources

On Schur complement of block diagonally dominant matrices

, 2006
It is well-known that the Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J.
Zhang, Cheng-yi, Chen, Feng, Li, Yao-tang   +2 more
core   +1 more source

A Schur complement approach to a general extrapolation algorithm

Linear Algebra and its Applications, 2003
The authors use Schur complements and their properties to obtain various interpretations of the E-transformation. It is proved that ratios of determinants similar to those appearing in the E-transformation can be recursively computed by a triangular recursive scheme and that, reciprocally, quantities computed by such a scheme can be expressed as a ...
BREZINSKI C, REDIVO ZAGLIA, MICHELA
openaire   +3 more sources

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

Output‐Feedback H∞$$ {H}_{\infty } $$ Detector‐Based Control of Continuous‐Time Markov Jump Lur'e Systems With Sector‐Bound Optimization

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This paper addresses the problem of dynamic output‐feedback H∞$$ {H}_{\infty } $$ detector‐based control for continuous‐time Markov Jump Lur'e Systems with uncertain transition rate matrices. In contrast to conventional approaches, the proposed synthesis conditions are derived using Finsler's lemma, introducing additional slack variables to ...
Lucas P. M. Silva, Cecilia F. Morais, Ricardo C. L. F. Oliveira   +2 more
wiley   +1 more source

Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices

, 2008
In this paper, we prove that the diagonal-Schur complement of a strictly doubly diagonally dominant matrix is strictly doubly diagonally dominant matrix.
Li, Jicheng, Liu, Jianzhou, Huang, Zhuohong, Kong, Xu   +3 more
core   +1 more source

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source

Optimization Problems of Hermitian Quadratic Matrix-Valued Functions and Applications

Axioms
In this paper, we investigate optimization problems for a Hermitian quadratic matrix-valued function involving two variable matrices. We derive algebraic formulas for the maximal and minimal ranks and partial inertias of this function based on a ...
Sihem Guerarra
doaj   +1 more source

Dynamic Resource Allocation Optimisation and Security‐Resilient Control for Bandwidth‐Limited Network Control Systems With Data Conflicts

CAAI Transactions on Intelligence Technology, EarlyView.
ABSTRACT Networked control systems (NCSs) often suffer from performance degradation due to limited communication bandwidth, which can cause data transmission conflicts and packet loss. Existing scheduling strategies may fail to simultaneously meet the real‐time requirements and the importance of multisensor data, and they are particularly vulnerable ...
Da Chen, Kaibo Shi, Bin Guo, Kangkang Sun, Huaicheng Yan, Xiao Cai   +5 more
wiley   +1 more source