scholarly journals An Improved Computationally Efficient Method for Finding the Drazin Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Haifa Bin Jebreen ◽  
Yurilev Chalco-Cano
Keyword(s):  
Efficient Method ◽  
Matrix Theory ◽  
Iterative Scheme ◽  
Drazin Inverse ◽  
Stability And Convergence ◽  
Computationally Efficient ◽  
Initial Matrix ◽  
The Matrix ◽  
The Stability

Drazin inverse is one of the most significant inverses in the matrix theory, where its computation is an intensive and useful task. The objective of this work is to propose a computationally effective iterative scheme for finding the Drazin inverse. The convergence is investigated analytically by applying a suitable initial matrix. The theoretical discussions are upheld by several experiments showing the stability and convergence of the proposed method.

scholarly journals Stability and Strong Convergence Results for Random Jungck-Kirk-Noor Iterative Scheme

2017 ◽  
Vol 58 (1) ◽  
pp. 167-182 ◽  
Author(s):  
R .A. Rashwan ◽  
H. A. Hammad
Keyword(s):  
Strong Convergence ◽  
Coincidence Point ◽  
Iterative Scheme ◽  
General Theorem ◽  
Stability And Convergence ◽  
Contractive Condition ◽  
Random Coincidence ◽  
Convergence Results ◽  
The Stability ◽  
Commuting Mappings

AbstractThe purpose of this study is to introduce a Jungck- Kirk-Noor type random iterative scheme and prove stability and strong convergence of this to establish a general theorem to approximate the unique common random coincidence point for two or more nonself random commuting mappings under general contractive condition in various spaces. Also we give the stability and convergence for random Jungck-Kirk-Ishikawa and random Jungck-Kirk-Mann as a corollaries. The results obtained in this paper improve the corresponding results announced recently.

Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations

2016 ◽  
Vol 19 (5) ◽  
pp. 1221-1241 ◽  
Author(s):  
Hua Wu ◽  
Jiajia Pan ◽  
Haichuan Zheng
Keyword(s):  
Domain Decomposition Method ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
One Dimensional ◽  
Collocation Points ◽  
The Matrix ◽  
Vorticity Equations ◽  
Legendre Spectral Method ◽  
Legendre Galerkin Method ◽  
The Stability

AbstractWe extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkin method while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and in parallel way. The numerical analysis results in the case of one-dimensional multi-domain are generalized to two-dimensional case. The stability and convergence of the method are proved. Numerical results are given.

scholarly journals On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2078
Author(s):  
Ajmal Ali ◽  
Thabet Abdeljawad ◽  
Azhar Iqbal ◽  
Tayyaba Akram ◽  
Muhammad Abbas
Keyword(s):  
Dirichlet Boundary ◽  
Iterative Scheme ◽  
Relaxation Method ◽  
Approximate Solutions ◽  
Dirichlet Boundary Conditions ◽  
Group Method ◽  
Numerical Tests ◽  
The Matrix ◽  
Fractional Group ◽  
The Stability

In this study, a new modified group iterative scheme for solving the two-dimensional (2D) fractional hyperbolic telegraph differential equation with Dirichlet boundary conditions is obtained from the 2h-spaced standard and rotated Crank–Nicolson FD approximations. The findings of new four-point modified explicit group relaxation method demonstrates the rapid rate of convergence of proposed method as compared to the existing schemes. Numerical tests are performed to test the capability of the group iterative scheme in comparison with the point iterative scheme counterparts. The stability of the derived modified group method is proven by the matrix norm algorithm. The obtained results are tabulated and concluded that exact solutions are exactly symmetric with approximate solutions.

New results for global stability of neutral-type delayed neural networks

2018 ◽  
Author(s):  
Neyir Ozcan
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Matrix Theory ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neural System ◽  
Delayed Neural Networks ◽  
The Matrix ◽  
The Stability ◽  
Stability Results

"This paper deals with the stability analysis of the class of neutral-type neural networks with constant time delay. By using a suitable Lyapunov functional, some delay independent sufficient conditions are derived, which ensure the global asymptotic stability of the equilibrium point for this this class of neutral-type neural networks with time delays with respect to the Lipschitz activation functions. The presented stability results rely on checking some certain properties of matrices. Therefore, it is easy to verify the validation of the constraint conditions on the network parameters of neural system by simply using some basic information of the matrix theory."

Estimating network edge probabilities by neighbourhood smoothing

Biometrika ◽  
2017 ◽  
Vol 104 (4) ◽  
pp. 771-783 ◽  
Author(s):  
Yuan Zhang ◽  
Elizaveta Levina ◽  
Ji Zhu
Keyword(s):  
Network Structure ◽  
Efficient Method ◽  
Error Rate ◽  
Adjacency Matrix ◽  
Link Prediction ◽  
Mean Squared Error ◽  
Smoothing Method ◽  
Computationally Efficient ◽  
Squared Error ◽  
The Matrix

Summary The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.

scholarly journals Partial Component Consensus of Discrete-Time Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Wenjun Hu ◽  
Gang Zhang ◽  
Zhongjun Ma ◽  
Binbin Wu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Matrix Theory ◽  
Pinning Control ◽  
Directed Network ◽  
Strong Function ◽  
Partial Stability ◽  
Partial Component ◽  
The Matrix ◽  
Error System

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

scholarly journals An Effective Potential for Frenkel Excitons

2020 ◽  
Author(s):  
Bartosz Błasiak ◽  
Wojciech Bartkowiak ◽  
Robert Władysław Góra
Keyword(s):  
Energy Transfer ◽  
Excitation Energy ◽  
Efficient Method ◽  
Effective Potential ◽  
Excitation Energy Transfer ◽  
Computationally Efficient ◽  
Frenkel Excitons

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is...

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

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