Results 31 to 40 of about 1,444 (195)

Inners and Schur complement

Linear Algebra and its Applications, 1978
AbstractIt is shown that for any square matrix having a left triangle of zeros, the determinants of its inners are equal to the leading principal minors of its Schur complement. In particular, if the original matrix has Sylvester-type form, then relationship between zero location theorems for polynomials are recovered.
Barnett, S., Jury, E.I.
openaire   +1 more source

Special H-matrices and their Schur and diagonal-Schur complements

Applied Mathematics and Computation, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cvetković, Ljiljana, Nedović, Maja
openaire   +4 more sources

Complementable operators and their Schur complements

Indian Journal of Pure and Applied Mathematics
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is invariably complementable. Additionally, we investigate the range-Hermitian property of these operators.
Naik, Sachin Manjunath, Johnson, P. Sam
openaire   +3 more sources

Solution Bounds and Numerical Methods of the Unified Algebraic Lyapunov Equation

Mathematics, 2022
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 ...
Juan Zhang, Shifeng Li, Xiangyang Gan
doaj   +1 more source

Voxel‐SLAM: A Complete, Accurate, and Versatile Light Detection and Ranging‐Inertial Simultaneous Localization and Mapping System

Advanced Intelligent Systems, EarlyView.
: In this work, Voxel‐SLAM (simultaneous localization and mapping) is introduced: a complete, accurate, and versatile LiDAR (light detection and ranging) ‐inertial SLAM system consisting of five modules: initialization, odometry, local mapping (LM), loop closure (LC), and global mapping (GM), all employing the same map representation, an adaptive voxel
Zheng Liu, Haotian Li, Chongjian Yuan, Xiyuan Liu, Jiarong Lin, Rundong Li, Chunran Zheng, Bingyang Zhou, Wenyi Liu, Fu Zhang   +9 more
wiley   +1 more source

Risk‐aware safe reinforcement learning for control of stochastic linear systems

Asian Journal of Control, EarlyView.
Abstract This paper presents a risk‐aware safe reinforcement learning (RL) control design for stochastic discrete‐time linear systems. Rather than using a safety certifier to myopically intervene with the RL controller, a risk‐informed safe controller is also learned besides the RL controller, and the RL and safe controllers are combined together ...
Babak Esmaeili, Nariman Niknejad, Hamidreza Modares   +2 more
wiley   +1 more source

Generalized Schur complements

Linear Algebra and its Applications, 1979
AbstractLet A be an n×n complex matrix. For a suitable subspace M of Cn the Schur compression A M and the (generalized) Schur complement A/M are defined. If A is written in the form A= BCST according to the decomposition Cn=M⊕M⊥ and if B is invertible, then AM=BCSSB−1C and A/M=000T−SB−1C· The commutativity rule for Schur complements is proved: (A/M)/N=(
openaire   +1 more source

Coupled Clustering in Hierarchical Matrices for the Oseen Problem

International Journal for Numerical Methods in Fluids, EarlyView.
Fluid flow problems can be modelled by the Navier‐Stokes or, after linearization, by the Oseen equations. Their discretization results in linear systems in saddle point form which are typically very large and need to be solved iteratively. We propose a novel block structure for hierarchical matrices which is then used to build preconditioners for the ...
Jonas Grams, Sabine Le Borne
wiley   +1 more source

Some Results on the Drazin Inverse of a Modified Matrix with New Conditions

International Journal of Analysis and Applications, 2014
In this article, we consider representations of the Drazin inverse of a modified matrix M = A−CDdB with the generalized Schur complement Z = D − BAdC under different conditions given in recent articles on the subject.
Abdul Shakoor, Hu Yang, Ilyas Ali
doaj   +2 more sources

Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices

Mathematics, 2023
It is necessary to explore more accurate estimates of the infinity norm of the inverse of a matrix in both theoretical analysis and practical applications.
Wenlong Zeng, Jianzhou Liu, Hongmin Mo
doaj   +1 more source