Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support v...Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models, this study takes cubic spline interpolation to generate a new polynomial smooth function ｜×｜ε^ 2, in g-insensitive support vector regression. Theoretical analysis shows that Sε^2 -function is better than pε^2 -function in properties, and the approximation accuracy of the proposed smoothing function is two order higher than that of classical pε^2 -function. The experimental data shows the efficiency of the new approach.展开更多
There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jorda...There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.展开更多
We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the ...We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.展开更多
The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where ...The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where G is a real simple Lie Group, W∈ g, C(W) 0 is the identity component of the centralizer C(W) of W in G .展开更多
基金The National Natural Science Foundations of China(11601409)the Natural Science Foundation of Shaanxi Province(2016JM1009)+3 种基金the Science Foundation of the Education Department of Shaanxi Province(17JK0344)the National Natural Science Foundation of Zhejiang Province(LY14A010007LQ14G010002)the Natural Science Foundation of Ningbo(2015A610173)
基金Supported by Guangdong Natural Science Foundation Project(No.S2011010002144)Province and Ministry Production and Research Projects(No.2012B091100497,2012B091100191,2012B091100383)+1 种基金Guangdong Province Enterprise Laboratory Project(No.2011A091000046)Guangdong Province Science and Technology Major Project(No.2012A080103010)
文摘Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models, this study takes cubic spline interpolation to generate a new polynomial smooth function ｜×｜ε^ 2, in g-insensitive support vector regression. Theoretical analysis shows that Sε^2 -function is better than pε^2 -function in properties, and the approximation accuracy of the proposed smoothing function is two order higher than that of classical pε^2 -function. The experimental data shows the efficiency of the new approach.
基金Supported by the National Science Foundation of China (19771006)
文摘There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.
基金supported by Hong Kong Research Grant Council(Grant No.Poly U5001/12p)National Natural Science Foundation of China(Grant No.11101231)
文摘We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.
文摘The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where G is a real simple Lie Group, W∈ g, C(W) 0 is the identity component of the centralizer C(W) of W in G .
