On the generally randomized extended Gauss-Seidel method

Author(s):  
Nianci Wu ◽  
Hua Xiang
Keyword(s):  
Author(s):  
Huina Song ◽  
Bowen Zhang ◽  
Mengyuan Wang ◽  
Yunhai Xiao ◽  
Liangliang Zhang ◽  
...  

2021 ◽  
Vol 32 (6) ◽  
pp. 1452-1464
Author(s):  
Afshin Ahmadi ◽  
Felice Manganiello ◽  
Amin Khademi ◽  
Melissa C. Smith
Keyword(s):  

2017 ◽  
Vol 36 (12) ◽  
pp. 1286-1311 ◽  
Author(s):  
Siddharth Choudhary ◽  
Luca Carlone ◽  
Carlos Nieto ◽  
John Rogers ◽  
Henrik I Christensen ◽  
...  

We consider the following problem: a team of robots is deployed in an unknown environment and it has to collaboratively build a map of the area without a reliable infrastructure for communication. The backbone for modern mapping techniques is pose graph optimization, which estimates the trajectory of the robots, from which the map can be easily built. The first contribution of this paper is a set of distributed algorithms for pose graph optimization: rather than sending all sensor data to a remote sensor fusion server, the robots exchange very partial and noisy information to reach an agreement on the pose graph configuration. Our approach can be considered as a distributed implementation of a two-stage approach that already exists, where we use the Successive Over-Relaxation and the Jacobi Over-Relaxation as workhorses to split the computation among the robots. We also provide conditions under which the proposed distributed protocols converge to the solution of the centralized two-stage approach. As a second contribution, we extend the proposed distributed algorithms to work with the object-based map models. The use of object-based models avoids the exchange of raw sensor measurements (e.g. point clouds or RGB-D data) further reducing the communication burden. Our third contribution is an extensive experimental evaluation of the proposed techniques, including tests in realistic Gazebo simulations and field experiments in a military test facility. Abundant experimental evidence suggests that one of the proposed algorithms (the Distributed Gauss–Seidel method) has excellent performance. The Distributed Gauss–Seidel method requires minimal information exchange, has an anytime flavor, scales well to large teams (we demonstrate mapping with a team of 50 robots), is robust to noise, and is easy to implement. Our field tests show that the combined use of our distributed algorithms and object-based models reduces the communication requirements by several orders of magnitude and enables distributed mapping with large teams of robots in real-world problems. The source code is available for download at https://cognitiverobotics.github.io/distributed-mapper/


2020 ◽  
Vol 2 (1) ◽  
pp. 1-8
Author(s):  
Nurullaeli Nurullaeli

The aim of this study is create an analysis media for calculating the electric current in a closed circuit with one or more loops.  Gauss-Jordan, Gauss-Seidel, and Cramer methods were used in this study. This media is packaged into Graphic User Interface (GUI) with matlab language program assisting. In this study, Linear Equation System (SPL) was obtained from kirchhoff current law and kirchhoff voltage law concepts.  Gauss-Seidel method is not always convergent for each formed SPL, because it can only be applied when coefficient matrix A was diagonally dominant. The application of this analysis media made the calculation of closed circuit electric current with one or more loops became accurate and time saving.


2021 ◽  
Vol 45 (02) ◽  
pp. 275-288
Author(s):  
MBE KOUA CHRISTOPHE NDJATCHI ◽  
PANAYOTIS VYRIDIS ◽  
JUAN MARTÍNEZ ◽  
J. JUAN ROSALES

In this paper, we study the boundary value problem on the unit circle for the Bratu’s equation depending on the real parameter μ. From the parameter estimate, the existence of non-negative solution is set. A numerical method is suggested to justify the theoretical result. It is a combination of the adaptation of finite difference and Gauss-Seidel method allowing us to obtain a good approximation of μc, with respect to the exact theoretical method μc = λ = 5.7831859629467.


2003 ◽  
Vol 22 (1) ◽  
Author(s):  
M.V.P. Garcia ◽  
C. Humes Jr. ◽  
J.M. Stern
Keyword(s):  

Author(s):  
I. V. Boikov ◽  
A. I. Boikova

Continuous Seidel method for solving systems of linear and nonlinear algebraic equations is constructed in the article, and the convergence of this method is investigated. According to the method discussed, solving a system of algebraic equations is reduced to solving systems of ordinary differential equations with delay. This allows to use rich arsenal of numerical ODE solution methods while solving systems of algebraic equations. The main advantage of the continuous analogue of the Seidel method compared to the classical one is that it does not require all the elements of the diagonal matrix to be non-zero while solving linear algebraic equations’ systems. The continuous analogue has the similar advantage when solving systems of nonlinear equations.


Sign in / Sign up

Export Citation Format

Share Document