Algorithm to construct integro splines

2021 ◽  
Vol 63 ◽  
pp. 359-375
Author(s):  
Renchin-Ochir Mijiddorj ◽  
Tugal Zhanlav
Keyword(s):  
Computational Complexity ◽  
Real Time ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Band Matrices ◽  
Low Computational Complexity ◽  
Computational Costs ◽  
The Given

We study some properties of integro splines. Using these properties, we design an algorithm to construct splines \(S_{m+1}(x)\) of neighbouring degrees to the given spline \(S_{m}(x)\) with degree \(m\). A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.   doi:10.1017/S1446181121000316

ALGORITHM TO CONSTRUCT INTEGRO SPLINES

2021 ◽  
pp. 1-17
Author(s):  
R. MIJIDDORJ ◽  
T. ZHANLAV
Keyword(s):  
Computational Complexity ◽  
Real Time ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Band Matrices ◽  
Low Computational Complexity ◽  
Computational Costs ◽  
The Given

Abstract We study some properties of integro splines. Using these properties, we design an algorithm to construct splines $S_{m+1}(x)$ of neighbouring degrees to the given spline $S_m(x)$ with degree m. A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.

scholarly journals Numerical Simulation of Fractional Control System Using Chebyshev Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Jun Zhang ◽  
Yugui Li ◽  
Jiaquan Xie
Keyword(s):  
Control System ◽  
Chebyshev Polynomials ◽  
Numerical Scheme ◽  
Original Problem ◽  
Linear Equations ◽  
Operational Matrix ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Fractional Control ◽  
The Given

In the current study, a numerical scheme based on Chebyshev polynomials is proposed to solve the problem of fractional control system. The operational matrix of fractional derivative is derived and that is used to transform the original problem into a system of linear equations. Lastly, several numerical examples are presented to verify the effectiveness and feasibility of the given method.

Solving systems of linear Boolean equations with noisy right-hand sides over the reals

2018 ◽  
Vol 28 (1) ◽  
pp. 1-5
Author(s):  
Evgeny K. Alekseev ◽  
Igor’ B. Oshkin ◽  
Vladimir O. Popov ◽  
Stanislav V. Smyshlyaev
Keyword(s):  
Random Vector ◽  
Theoretical Calculations ◽  
Linear Equations ◽  
Random Variable ◽  
System Of Linear Equations ◽  
Right Hand ◽  
The Given ◽  
Normally Distributed

Abstract The paper is concerned with the problem of solution of a system of linear equations with noisy right-hand side in the following setting: one knows a random m × N-matrix A with entries from {–1, 1} and a vector xA + ξ ∈ ℝN, where ξ is the noise vector from ℝN, whose entries are independent realizations of a normally distributed random variable with parameters 0 and σ2, and x is a random vector with coordinates from {–1, 1}. The sought-for parameter is the vector x. We propose a method for constructing a set containing the sought-for vector with probability not smaller than the given one and estimate the cardinality of this set. Theoretical calculations of the parameters of the method are illustrated by experiments demonstrating the practical implementability of the method for cases when direct enumeration of all possible values of x is unfeasible.

scholarly journals Improved Real-Time Facial Expression Recognition Based on a Novel Balanced and Symmetric Local Gradient Coding

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1899 ◽  
Author(s):  
Jucheng Yang ◽  
Xiaojing Wang ◽  
Shujie Han ◽  
Jie Wang ◽  
Dong Sun Park ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Facial Expression ◽  
Real Time ◽  
Facial Expression Recognition ◽  
Recognition Rate ◽  
Expression Recognition ◽  
Low Computational Complexity ◽  
Local Texture ◽  
Local Gradient ◽  
Texture Coding

In the field of Facial Expression Recognition (FER), traditional local texture coding methods have a low computational complexity, while providing a robust solution with respect to occlusion, illumination, and other factors. However, there is still need for improving the accuracy of these methods while maintaining their real-time nature and low computational complexity. In this paper, we propose a feature-based FER system with a novel local texture coding operator, named central symmetric local gradient coding (CS-LGC), to enhance the performance of real-time systems. It uses four different directional gradients on 5 × 5 grids, and the gradient is computed in the center-symmetric way. The averages of the gradients are used to reduce the sensitivity to noise. These characteristics lead to symmetric of features by the CS-LGC operator, thus providing a better generalization capability in comparison to existing local gradient coding (LGC) variants. The proposed system further transforms the extracted features into an eigen-space using a principal component analysis (PCA) for better representation and less computation; it estimates the intended classes by training an extreme learning machine. The recognition rate for the JAFFE database is 95.24%, whereas that for the CK+ database is 98.33%. The results show that the system has advantages over the existing local texture coding methods.

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