Research

746 KiB

Open AccessArticle

A Five-Point Subdivision Scheme with Two Parameters and a Four-Point Shape-Preserving Scheme

by Jieqing Tan, Bo Wang and Jun Shi

Math. Comput. Appl. 2017, 22(1), 22; https://doi.org/10.3390/mca22010022 - 24 Feb 2017

Cited by 5 | Viewed by 3902

In order to improve the flexibility of curves, a new five-point binary approximating subdivision scheme with two parameters is presented. The generating polynomial method is used to investigate the uniform convergence and

C^{k}

-continuity of this scheme. In a special case, the [...] Read more.

In order to improve the flexibility of curves, a new five-point binary approximating subdivision scheme with two parameters is presented. The generating polynomial method is used to investigate the uniform convergence and

C^{k}

-continuity of this scheme. In a special case, the five-point scheme changes into a four-point scheme, which can generate

C^{3}

limit curves. The shape-preserving properties of the four-point scheme are analyzed, and a few examples are given to illustrate the efficiency and the shape-preserving effect of this special case. Full article

(This article belongs to the Special Issue Information and Computational Science)

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239 KiB

Open AccessArticle

Global Modulus-Based Synchronous Multisplitting Multi-Parameters TOR Methods for Linear Complementarity Problems

by Li-Tao Zhang and Tong-Xiang Gu

Math. Comput. Appl. 2017, 22(1), 20; https://doi.org/10.3390/mca22010020 - 21 Feb 2017

Viewed by 2965

Abstract

In 2013, Bai and Zhang constructed modulus-based synchronous multisplitting methods for linear complementarity problems and analyzed the corresponding convergence. In 2014, Zhang and Li studied the weaker convergence results based on linear complementarity problems. In 2008, Zhang et al. presented global relaxed non-stationary [...] Read more.

In 2013, Bai and Zhang constructed modulus-based synchronous multisplitting methods for linear complementarity problems and analyzed the corresponding convergence. In 2014, Zhang and Li studied the weaker convergence results based on linear complementarity problems. In 2008, Zhang et al. presented global relaxed non-stationary multisplitting multi-parameter method by introducing some parameters. In this paper, we extend Bai and Zhang’s algorithms and analyze global modulus-based synchronous multisplitting multi-parameters TOR (two parameters overrelaxation) methods. Moverover, the convergence of the corresponding algorithm in this paper are given when the system matrix is an

H_{+}

-matrix. Full article

(This article belongs to the Special Issue Information and Computational Science)

238 KiB

Open AccessArticle

Rape Plant Disease Recognition Method of Multi-Feature Fusion Based on D-S Evidence Theory

by Min Hu, Xiangyu Bu, Xiao Sun, Zixi Yu and Yaona Zheng

Math. Comput. Appl. 2017, 22(1), 18; https://doi.org/10.3390/mca22010018 - 15 Feb 2017

Cited by 7 | Viewed by 3636

Abstract

In view of the low accuracy and uncertainty of the traditional rape plant disease recognition relying on a single feature, this paper puts forward a rape plant disease recognition method based on Dempster-Shafer (D-S) evidence theory and multi-feature fusion. Firstly, color matrix and [...] Read more.

In view of the low accuracy and uncertainty of the traditional rape plant disease recognition relying on a single feature, this paper puts forward a rape plant disease recognition method based on Dempster-Shafer (D-S) evidence theory and multi-feature fusion. Firstly, color matrix and gray-level co-occurrence matrix are extracted as two kinds of features from rape plant images after processing. Then by calculating the Euclidean distance between the test samples and training samples, the basic probability assignment function can be constructed. Finally, the D-S combination rule of evidence is used to achieve fusion, and final recognition results are given by using the variance. This method is used to collect rape plant images for disease recognition, and recognition rate arrives at 97.09%. Compared with other methods, experimental results show that the method is more effective and with lower computational complexity. Full article

(This article belongs to the Special Issue Information and Computational Science)

1377 KiB

Open AccessArticle

Analysis of Inflection and Singular Points on a Parametric Curve with a Shape Factor

by Zhi Liu, Chen Li, Jieqing Tan and Xiaoyan Chen

Math. Comput. Appl. 2017, 22(1), 9; https://doi.org/10.3390/mca22010009 - 19 Jan 2017

Cited by 5 | Viewed by 4088

Abstract

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived [...] Read more.

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely characterized by the relative position of the edge vectors of the control polygon and the shape factor. The results are summarized in a shape diagram, which is useful when the cubic parametric curves are used for geometric modeling. Furthermore, we discuss the influences of the shape factor on the shape diagram and the ability for adjusting the shape of the curve. Full article

(This article belongs to the Special Issue Information and Computational Science)

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763 KiB

Open AccessArticle

A New Approximation Method with High Order Accuracy

by Ziwu Jiang

Math. Comput. Appl. 2017, 22(1), 11; https://doi.org/10.3390/mca22010011 - 19 Jan 2017

Cited by 1 | Viewed by 3101

Abstract

In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and [...] Read more.

In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produces higher accuracy compared with other approaches. Numerical examples demonstrate that the proposed scheme is effective. Full article

(This article belongs to the Special Issue Information and Computational Science)

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1188 KiB

Open AccessArticle

Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications

by Rengui Yu, Chungang Zhu, Xianmin Hou and Li Yin

Math. Comput. Appl. 2017, 22(1), 10; https://doi.org/10.3390/mca22010010 - 19 Jan 2017

Cited by 2 | Viewed by 3530

Abstract

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces

S_{5}^{3} (Δ_{m n}^{(2)})

. Moreover, the properties [...] Read more.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces

S_{5}^{3} (Δ_{m n}^{(2)})

. Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving the two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results. Full article

(This article belongs to the Special Issue Information and Computational Science)

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1247 KiB

Open AccessArticle

VRP-GMRES(m) Iteration Algorithm for Fast Multipole Boundary Element Method

by Chunxiao Yu, Cuihuan Ren and Xueting Bai

Math. Comput. Appl. 2016, 21(4), 49; https://doi.org/10.3390/mca21040049 - 13 Dec 2016

Cited by 3 | Viewed by 3803

Abstract

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES(m)) algorithm with Variable Restart Parameter (VRP-GMRES(m)) algorithm is proposed. By properly changing a variable restart parameter for [...] Read more.

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES(m)) algorithm with Variable Restart Parameter (VRP-GMRES(m)) algorithm is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector

r_{m + 1}

on

r_{m}

is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing. Full article

(This article belongs to the Special Issue Information and Computational Science)

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1416 KiB

Open AccessArticle

Rational Spline Image Upscaling with Constraint Parameters

by Xunxiang Yao, Yunfeng Zhang, Fangxun Bao and Caiming Zhang

Math. Comput. Appl. 2016, 21(4), 48; https://doi.org/10.3390/mca21040048 - 13 Dec 2016

Cited by 5 | Viewed by 3564

Abstract

Image interpolation is one of key contents in image processing. We present an interpolation algorithm based on a rational function model with constraint parameters. Firstly, based on the construction principle of the rational function, the detection threshold is selected through contour analysis. The [...] Read more.

Image interpolation is one of key contents in image processing. We present an interpolation algorithm based on a rational function model with constraint parameters. Firstly, based on the construction principle of the rational function, the detection threshold is selected through contour analysis. The smooth and non-smooth areas are interpolated by bicubic interpolation and general rational interpolation, respectively. In order to enhance the contrast in non-smooth areas and preserve the details, the parameter optimization technique is applied to get optimal shape parameters. Experimental results on benchmark test images demonstrate that the proposed method achieves competitive performance with the state-of-the-art interpolation algorithms, especially in image details and texture features. Full article

(This article belongs to the Special Issue Information and Computational Science)

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