14 Results Found

By using the maximal and minimal ranks of some generalized Schur complement, the equivalent conditions for the reverse order law $\left(AB\right)\{1,3M,4K\}=B\{1,3N,4K\}A\{1,3M,4N\}$ are presented.

The generalized inverse has numerous important applications in aspects of the theoretic research of matrices and statistics. One of the core problems of generalized inverse is finding the necessary and sufficient conditions for the reverse (or the fo...

The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order l...

The forward order law for generalized inverses has potential applications in numerical linear algebra, control theory, and statistics. This topic has attracted considerable attention. In this article, we present a necessary and sufficient condition f...

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 line...

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix, which, in turn, constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the d...

Based on the Schur complement, some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant matrices are obtained. In addition, it is shown that the new bound improves the previous bounds. Numerical exampl...

In this paper, applying some properties of matrix inequality and Schur complement, we give new upper and lower bounds of the solution for the unified algebraic Lyapunov equation that generalize the forms of discrete and continuous Lyapunov matrix equ...

This article designs an observer for the joint estimation of the state and the unknown input for a class of nonlinear fractional-order systems (FOSs) such that one portion satisfies the Lipschitz condition and the other does not necessarily satisfy s...

Representing the uncertainties with a set of scenarios, the optimization problem resulting from a robust nonlinear model predictive control (NMPC) strategy at each sampling instance can be viewed as a large-scale stochastic program. This paper solves...

A new class of high-performance preconditioned iterative solution methods for large-scale finite element method (FEM) elliptic systems is proposed and analyzed. The non-overlapping domain decomposition (DD) naturally introduces coupling operator at t...

The model-based polarimetric synthetic aperture radar (PolSAR) target decomposition decodes the scattering mechanism of the target by analyzing the essential scattering components. This paper presents a new general three-component scattering power de...

Seismoelectric responses generated in fluid-saturated porous media contain indirect geophysical information related to subsurface interfaces, material contrasts, and electrokinetic coupling. Many three-dimensional simulations adopt a quasi-static ele...

To enable autonomous route planning for UAV swarms in dynamic air–terrestrial cooperative navigation scenarios within GNSS-denied environments, this paper proposes a lightweight framework based on the Artificial Potential Field (APF) method. In...