We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex dif...We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.展开更多
We study the optimal order of approximation for |x|α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.
微分方程的计算求解在计算机工程上有重要的理论意义和应用价值。针对传统数值解法计算复杂度高、解的形式离散等问题,本文基于微分方程的回归方程观点与解法,应用统计回归方法求解二阶常微分方程,并给出基于中心支持向量机(proximal su...微分方程的计算求解在计算机工程上有重要的理论意义和应用价值。针对传统数值解法计算复杂度高、解的形式离散等问题,本文基于微分方程的回归方程观点与解法,应用统计回归方法求解二阶常微分方程,并给出基于中心支持向量机(proximal support vector machine,P-SVM)在常微分方程的初值和边值问题上的近似解求法。通过在目标优化函数中添加偏置项,构建P-SVM回归模型,从而避免大规模求解线性方程组,得到结构简洁的最优解表达式。模型通过最小化训练样本点的均方误差和,在保证精度的同时,有效提高了近似解的计算速度。此外,形式简洁固定的解析解表达式也便于在实际应用中进行定性分析和性质研究。数值试验结果验证了P-SVM方法是一种高效可行的常微分方程求解方法。展开更多
基金Project Supported by the Natural Science Foundation of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.
文摘We study the optimal order of approximation for |x|α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.
文摘微分方程的计算求解在计算机工程上有重要的理论意义和应用价值。针对传统数值解法计算复杂度高、解的形式离散等问题,本文基于微分方程的回归方程观点与解法,应用统计回归方法求解二阶常微分方程,并给出基于中心支持向量机(proximal support vector machine,P-SVM)在常微分方程的初值和边值问题上的近似解求法。通过在目标优化函数中添加偏置项,构建P-SVM回归模型,从而避免大规模求解线性方程组,得到结构简洁的最优解表达式。模型通过最小化训练样本点的均方误差和,在保证精度的同时,有效提高了近似解的计算速度。此外,形式简洁固定的解析解表达式也便于在实际应用中进行定性分析和性质研究。数值试验结果验证了P-SVM方法是一种高效可行的常微分方程求解方法。
