The Experts below are selected from a list of 6771 Experts worldwide ranked by ideXlab platform
Guozhao Wang - One of the best experts on this subject based on the ideXlab platform.
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triangular domain extension of linear bernstein like Trigonometric Polynomial basis
Journal of Zhejiang University Science C, 2010Co-Authors: Wanqiang Shen, Guozhao WangAbstract:In computer aided geometric design (CAGD), the Bernstein-Bezier system for Polynomial space including the triangular domain is an important tool for modeling free form shapes. The Bernstein-like bases for other spaces (Trigonometric Polynomial, hyperbolic Polynomial, or blended space) has also been studied. However, none of them was extended to the triangular domain. In this paper, we extend the linear Trigonometric Polynomial basis to the triangular domain and obtain a new Bernstein-like basis, which is linearly independent and satisfies positivity, partition of unity, symmetry, and boundary representation. We prove some properties of the corresponding surfaces, including differentiation, subdivision, convex hull, and so forth. Some applications are shown.
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Trigonometric Polynomial b spline with shape parameter
Progress in Natural Science, 2004Co-Authors: Wentao Wang, Guozhao WangAbstract:The basis function of n order Trigonometric Polynomial B-spline with shape parameter is constructed by an integral approach. The shape of the constructed curve can be adjusted by changing the shape parameter and it has most of the properties of B-spline. The ellipse and circle can be accurately represented by this basis function.
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uniform Trigonometric Polynomial b spline curves
Science in China Series F: Information Sciences, 2002Co-Authors: Guozhao Wang, Xunnian YangAbstract:This paper presents a new kind of uniform spline curve, named Trigonometric Polynomial B-splines, over spaceΩ = span{sint, cost,t k−3,t k−4, …,t, 1} of whichk is an arbitrary integer larger than or equal to 3. We show that Trigonometric Polynomial B-spline curves have many similar properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both Polynomial curves and Trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.
Xuli Han - One of the best experts on this subject based on the ideXlab platform.
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A Practical Method for Generating Trigonometric Polynomial Surfaces over Triangular Domains
Mediterranean Journal of Mathematics, 2015Co-Authors: Xuli Han, Yuanpeng ZhuAbstract:A class of Trigonometric Polynomial basis functions over triangular domain with three shape parameters is constructed in this paper. Based on these new basis functions, a kind of Trigonometric Polynomial patch over triangular domain, which can be used to construct some surfaces whose boundaries are arcs of ellipse or parabola, is proposed. Without changing the control points, the shape of the Trigonometric Polynomial patch can be adjusted flexibly in a foreseeable way using the shape parameters. For computing the proposed Trigonometric Polynomial patch stably and efficiently, a practical de Casteljau-type algorithm is developed. Moveover, the conditions for G 1 continuous smooth joining two Trigonometric Polynomial patches are deduced.
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Normalized B-basis of the space of Trigonometric Polynomials and curve design
Applied Mathematics and Computation, 2015Co-Authors: Xuli HanAbstract:A normalized B-basis of the space of Trigonometric Polynomials of degree n is presented. Some interesting properties of the basis functions are given. Based on the basis, symmetric Trigonometric Polynomial curves like Bezier curves are constructed. The Trigonometric Polynomial curves present the shape of their control polygons well. Thus the theoretics and methods are proposed for curve representation of the Trigonometric Polynomial space. By adding additional control points, the given graph examples show that the Trigonometric Polynomial curves are nearer their control polygons than the Bezier curves for the same parametric variable and the same degree.
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The Trigonometric Polynomial like Bernstein Polynomial.
TheScientificWorldJournal, 2014Co-Authors: Xuli HanAbstract:A symmetric basis of Trigonometric Polynomial space is presented. Based on the basis, symmetric Trigonometric Polynomial approximants like Bernstein Polynomials are constructed. Two kinds of nodes are given to show that the Trigonometric Polynomial sequence is uniformly convergent. The convergence of the derivative of the Trigonometric Polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of Trigonometric Polynomials are constructed. Some interesting properties of the Trigonometric Polynomials are given.
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quadratic Trigonometric Polynomial curves concerning local control
Applied Numerical Mathematics, 2006Co-Authors: Xuli HanAbstract:With a non-uniform knot vector and two local shape parameters, a kind of piecewise quadratic Trigonometric Polynomial curves is presented in this paper. The given curves have similar construction and the same continuity as the quadratic non-uniform B-spline curves. Two local parameters serve to local control tension and local control bias respectively in the curves. The changes of a local shape parameter will only affect two curve segments. The given curves can approximate the quadratic non-uniform rational B-spline curves and the quadratic rational Bezier curves well for which the relations of the local shape parameters and the weight numbers of the rational curves are described. The Trigonometric Polynomial curves can yield tight envelopes for the quadratic rational Bezier curves. The given curve also can be decreased to linear Trigonometric Polynomial curve which is equal to a quadratic rational Bezier curve and represents ellipse curve.
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c2 quadratic Trigonometric Polynomial curves with local bias
Journal of Computational and Applied Mathematics, 2005Co-Authors: Xuli HanAbstract:Quadratic Trigonometric Polynomial curves with local bias are presented in this paper. The quadratic Trigonometric Polynomial curves have C^2 continuity with a non-uniform knot vector and any value of the bias, while the quadratic B-spline curves have C^1 continuity. The changes of a local bias parameter will only affect two curve segments. With the bias parameters, the quadratic Trigonometric Polynomial curves can move locally toward or against a control vertex. A quadratic Trigonometric Bezier curve is also introduced as special case of the given Trigonometric Polynomial curves.
John Fulcher - One of the best experts on this subject based on the ideXlab platform.
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financial prediction using higher order Trigonometric Polynomial neural network group model
Proceedings of International Conference on Neural Networks (ICNN'97), 1997Co-Authors: Jing Chun Zhang, Ming Zhang, John FulcherAbstract:A higher order Trigonometric Polynomial neural network group model (HTG) which can be used for financial prediction is discussed in this paper. HTG is written in C, incorporates a user-friendly graphical user interface, and runs under XWindows on a Sun workstation. The experimental results show that HTG is able to handle higher frequency, higher order nonlinear and discontinuous data. The accuracy of HTG is around 5% to 10% better than conventional Trigonometric Polynomial neural network models.
Hidemitsu Ogawa - One of the best experts on this subject based on the ideXlab platform.
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active learning with model selection simultaneous optimization of sample points and models for Trigonometric Polynomial models
IEICE Transactions on Information and Systems, 2003Co-Authors: Masashi Sugiyama, Hidemitsu OgawaAbstract:In supervised learning, the selection of sample points and models is crucial for acquiring a higher level of the generalization capability. So far, the problems of active learning and model selection have been independently studied. If sample points and models are simultaneously optimized, then a higher level of the generalization capability is expected. We call this problem active learning with model selection. However, active learning with model selection can not be generally solved by simply combining existing active learning and model selection techniques because of the active learning / model selection dilemma: the model should be fixed for selecting sample points and conversely the sample points should be fixed for selecting models. In this paper, we show that the dilemma can be dissolved if there is a set of sample points that is optimal for all models in consideration. Based on this idea, we give a practical procedure for active learning with model selection in Trigonometric Polynomial models. The effectiveness of the proposed procedure is demonstrated through computer simulations.
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active learning for optimal generalization in Trigonometric Polynomial models
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2001Co-Authors: Masashi Sugiyama, Hidemitsu OgawaAbstract:In this paper, we consider the problem of active learning, and give a necessary and sufficient condition of sample points for the optimal generalization capability. By utilizing the properties of pseudo orthogonal bases, we clarify the mechanism of achieving the optimal generalization capability. We also show that the condition does not only provide the optimal generalization capability but also reduces the computational complexity and memory required for calculating learning result functions. Based on the optimality condition, we give design methods of optimal sample points for Trigonometric Polynomial models. Finally, the effectiveness of the proposed active learning method is demonstrated through computer simulations.
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training data selection for optimal generalization in Trigonometric Polynomial networks
Neural Information Processing Systems, 1999Co-Authors: Masashi Sugiyama, Hidemitsu OgawaAbstract:In this paper, we consider the problem of active learning in Trigonometric Polynomial networks and give a necessary and sufficient condition of sample points to provide the optimal generalization capability. By analyzing the condition from the functional analytic point of view, we clarify the mechanism of achieving the optimal generalization capability. We also show that a set of training examples satisfying the condition does not only provide the optimal generalization but also reduces the computational complexity and memory required for the calculation of learning results. Finally, examples of sample points satisfying the condition are given and computer simulations are performed to demonstrate the effectiveness of the proposed active learning method.
Jing Chun Zhang - One of the best experts on this subject based on the ideXlab platform.
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Artificial Higher Order Neural Networks for Economics and Business - Trigonometric Polynomial Higher Order Neural Network Group Models and Weighted Kernel Models for Financial Data Simulation and Prediction
Artificial Higher Order Neural Networks for Economics and Business, 2009Co-Authors: Lei Zhang, Simeon J. Simoff, Jing Chun ZhangAbstract:This chapter introduces Trigonometric Polynomial higher order neural network models. In the area of financial data simulation and prediction, there is no single neural network model that could handle the wide variety of data and perform well in the real world. A way of solving this difficulty is to develop a number of new models, with different algorithms. A wider variety of models would give financial operators more chances to find a suitable model when they process their data. That was the major motivation for this chapter. The theoretical principles of these improved models are presented and demonstrated and experiments are conducted by using real-life financial data.
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financial prediction using higher order Trigonometric Polynomial neural network group model
Proceedings of International Conference on Neural Networks (ICNN'97), 1997Co-Authors: Jing Chun Zhang, Ming Zhang, John FulcherAbstract:A higher order Trigonometric Polynomial neural network group model (HTG) which can be used for financial prediction is discussed in this paper. HTG is written in C, incorporates a user-friendly graphical user interface, and runs under XWindows on a Sun workstation. The experimental results show that HTG is able to handle higher frequency, higher order nonlinear and discontinuous data. The accuracy of HTG is around 5% to 10% better than conventional Trigonometric Polynomial neural network models.
