scholarly journals Gauss–Seidel method with oblique direction

2021 ◽  
Vol 12 ◽  
pp. 100180
Author(s):  
Fang Wang ◽  
Weiguo Li ◽  
Wendi Bao ◽  
Zhonglu Lv
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):  

Being engaged in collecting materials for a work entitled “A Picture of Naval Architecture in the 18th and 19th Centuries,” the author was induced to visit this country, with a view to become acquainted with the various innovations and improvements lately introduced here in the art of ship-building; and, in the present communication, offers some remarks upon the plans proposed by Mr. Seppings, an account of which has formerly been before the Royal Society, and is printed in their Transactions for 1814. After giving an outline of the fundamental principles upon which Mr. Seppings’s improvements in naval architecture principally depend, and dwelling especially upon the diagonal pieces of timber which he employs to strengthen the usual rectangular frame-work, the author proceeds to state that similar contrivances were long ago suggested and even practised by the French ship-builders, in order to give strength to the general fabric of their vessels. Instead of making the ceiling parallel to the exterior planks, they arranged it in the oblique direction of the diagonals of the parallelograms formed by the timber and the ceiling, in the whole of that part of the ship’s sides between the orlop and limber-strake next the kelson. They then covered this ceiling with riders, as usual, and placed crosspieces between them in the direction of the second diameter of the parallelogram. This system, however, was abandoned in the French navy, on account of its expense, of its diminishing the capacity of the hold, and of the erroneous notion that the longitudinal length of the ship was diminished by the obliquity of the ceiling. In 1755, the Academy of Sciences rewarded M. Chauchot, a naval engineer, for the suggestion of employing oblique for transverse riders; and in 1772, M. Clairon des Lauriers employed diagonal strengtheners in the construction of the frigate l’Oiseau.


1974 ◽  
Vol 40 (479) ◽  
pp. 1099-1104
Author(s):  
Sakiichi OKABE ◽  
Yasuo YOKOYAMA ◽  
Yasuo JIMBO
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):  

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