scholarly journals Linear Equations, Inequalities, Linear Programs, and a New Efficient Algorithm

2006 ◽  
pp. 1-36 ◽  
Author(s):  
Katta G. Murty
Keyword(s):  
Efficient Algorithm ◽  
Linear Equations ◽  
Linear Programs

scholarly journals Improved Heuristics for Short Linear Programs

2019 ◽  
pp. 203-230
Author(s):  
Quan Quan Tan ◽  
Thomas Peyrin
Keyword(s):  
Random Matrices ◽  
Selection Criteria ◽  
Block Cipher ◽  
State Of The Art ◽  
Linear Equations ◽  
Linear Programs ◽  
System Of Linear Equations ◽  
New Methods ◽  
The Matrix

In this article, we propose new heuristics for minimising the amount of XOR gates required to compute a system of linear equations in GF(2). We first revisit the well known Boyar-Peralta strategy and argue that a proper randomisation process during the selection phases can lead to great improvements. We then propose new selection criteria and explain their rationale. Our new methods outperform state-of-the-art algorithms such as Paar or Boyar-Peralta (or open synthesis tools such as Yosys) when tested on random matrices with various densities. They can be applied to matrices of reasonable sizes (up to about 32 × 32). Notably, we provide a new implementation record for the matrix underlying the MixColumns function of the AES block cipher, requiring only 94 XORs.

A New and Efficient Algorithm for the Inverse Kinematics of a General Serial 6R

2005 ◽  
Author(s):  
Manfred L. Husty ◽  
Martin Pfurner ◽  
Hans-Peter Schro¨cker
Keyword(s):  
Efficient Algorithm ◽  
Inverse Kinematics ◽  
Linear Equations ◽  
Main Idea ◽  
Kinematic Chain ◽  
Joint Angles ◽  
Degree Polynomial ◽  
Geometric Information ◽  
Multidimensional Geometry ◽  
Dimensional Projective Space

In this paper a new and very efficient algorithm to compute the inverse kinematics of a general 6R serial kinematic chain is presented. The main idea is to make use of classical multidimensional geometry to structure the problem and to use the geometric information before starting the elimination process. For the geometric preprocessing we use the Study model of Euclidean displacements, sometimes called kinematic image, which identifies a displacement with a point on a six dimensional quadric S62 in seven dimensional projective space P7. The 6R chain is broken up in the middle to form two open 3R chains. The kinematic image of a 3R chain turns out to be a Segre-manifold consisting of a one parameter set of 3-spaces. The intersection of two Segre-manifolds and S62 yields 16 points which are the kinematic images representing the 16 solutions of the inverse kinematics. Algebraically this procedure means that we have to solve a system of seven linear equations and one resultant to arrive at the univariate 16 degree polynomial. From this step in the algorithm we get two out of the six joint angles and the remaining 4 angles are obtained straight forward by solving the inverse kinematics of two 2R chains.

scholarly journals Efficient Algorithm for the Computation of the Solution to a Sparse Matrix Equation in Distributed Control Theory

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1497
Author(s):  
Leonardo Pedroso ◽  
Pedro Batista
Keyword(s):  
Distributed Control ◽  
Matrix Equation ◽  
Efficient Algorithm ◽  
State Of The Art ◽  
Sparse Matrix ◽  
Linear Equations ◽  
Real Life ◽  
The State ◽  
Wide Range ◽  
Estimation And Control

In this short communication, an algorithm for efficiently solving a sparse matrix equation, which arises frequently in the field of distributed control and estimation theory, is proposed. The efficient algorithm stems from the fact that the sparse equation at hand can be reduced to a system of linear equations. The proposed algorithm is shown to require significantly fewer floating point operations than the state-of-the-art solution. The proposed solution is applied to a real-life example, which models a wide range of industrial processes. The experimental results show that the solution put forward allows for a significant increase in efficiency in relation to the state-of-the-art solution. The significant increase in efficiency of the presented algorithm allows for a valuable widening of the applications of distributed estimation and control.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

The influence of extrinsic motivation and work experience on employee performance (Case study in the Serang Baru Sub-district, Bekasi District)

2020 ◽  
Vol 5 (02) ◽  
pp. 167
Author(s):  
Nur’enny Nur’enny ◽  
Rahmat Hidayat
Keyword(s):  
Work Experience ◽  
Extrinsic Motivation ◽  
Employee Performance ◽  
Linear Equations ◽  
Test Reliability ◽  
Coefficient Of Determination ◽  
District Office ◽  
Normality Test ◽  
Observation Methods ◽  
Saturated Sample

This study aims to obtain information about extrinsic motivation and work experience and its effect on employee performance in the Serang Baru District Office. This study uses a saturated sample so that the population is the same as the sample of 80 employees, at the Serang Baru District Office. The method used is validation test, reliability test, then classical assumption test, which includes normality test and multicollinearity, as well as heteroscedasticity test, multiple linear analysis test, multiple linear equations, F test, coefficient of determination, and t test. The data of this research used observation methods and questionnaires distributed to 80 samples which were addressed to employees of the Serang Baru District Office. Based on the results of research and discussion, it can be concluded: 1) Extrinsic motivation does not affect employee performance because employees are willing to work more than expected regardless of extrinsic motivation or not. 2) Employee performance is strongly influenced by work experience. The more experience, they get while working, the more knowledge they will get. 3) Employee performance will be better with the support of experienced employees so as to increase the level of output produced.             Keywords: Employee Performance, Extrinsic Motivation, Work Experience

Optimization of Linear Equations using Genetic Algorithms

2011 ◽  
Vol 2 (3) ◽  
pp. 56-58
Author(s):  
Roshni .V Patel ◽  
◽  
Jignesh. S Patel
Keyword(s):  
Genetic Algorithms ◽  
Linear Equations
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